Research ArticleInventory Control Systems Model forStrategic Capacity Acquisition

Anthony S White and Michael Censlive

School of Science and Technology Middlesex University The Burroughs Hendon London NW4 4BT UK

Correspondence should be addressed to Anthony S White awhitemdxacuk

Received 20 June 2016 Revised 18 September 2016 Accepted 12 October 2016

Academic Editor Uday Venkatadri

Copyright copy 2016 A S White and M CensliveThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Variation of installed industrial capacity has been found to follow a cyclic pattern This paper discusses the application of controltheory to the problem of the timely acquisition of extra production capacity The control system based model presented here iscompared with a SystemDynamicsmodel proposed by Sterman Key differences are themethod of implementing rational decisionsabout deployment of extra capacity and the use of a nonlinear APVIOBPCS inventory model Benefits of this new model are amore measurable process and the ability to select parameter values to optimise capacity deployment Simulation of the modelindicates that the results found by Sterman underestimate the production backlog and time taken to reach equilibriumThe use ofa Proportional Integral and Derivative (PID) controller in the capacity control loop model illustrates that it is possible not only toalter the backlog levels but at the same time to reduce the sales force and improve the revenueThemodel also shows clearly that theimpact of not increasing capacity promptly results in catastrophic failure of sales as a structural rather than a business problemThis model is simple enough to be implemented as a spreadsheet for use as a guide by managers

1 Introduction

Todayrsquos consumer market is dominated by two main factorsone is the need for rapid development of new productsand the other is the need for an equally rapid response tomarket led demand Business cycles have long dominatedeconomic analysis but most researchers have concentratedon examining the average effects on the economy discussingthe long term expansion and decline of the whole system(Sterman and Mosekilde [1] King and Rebelo [2] and Euro-pean Commission [3]) These reports confirm the existenceof cycles that vary over a period of less than one year invarious sectors of the economy Sterman ([4] pp 792ndash797)shows that similar cyclical changes occur in many industrysectors over a number of years His analysis using SystemDynamics (SD) illustrates that these cycles are due to thestructure of the system and not primarily due to outside(exogenous) circumstances One of the principle conclusionsof SD analysis is that all businesses operate under very similardynamics Stermanrsquos [5] work on decisionsmade bymanagersusing a ldquoFlight Simulatorrdquo approach to operating supply

chains shows how those decisions affect the dynamics ofthe operation often causing severe oscillatory performanceDecisions based on small changes in the appreciation ofthe market conditions have severe effects on the wholeprocess In particular managers appear unable to forecastthe behaviour of systems which have considerable delaysLyneis [6] reported a number of general lessons gainedfrom the ldquoFlight Simulatorrdquo including failing to account forcompetitive response and mistaking forecasts for realityThismisperception of feedback bymanagers was also used by Lan-gley et al [7] to explain capacity overshoot Companies haveto make strategic market-based decisions about the capacityof their plant in relatively rapidly changing circumstancesas well as catering for customer preferences Forrester [8]shortly after inventing System Dynamics devised marketgrowth models to test how rational decisions would affectmarket performance These models were devised in orderto advise entrepreneurs as well as high-tech companiesand were intended to examine the observation that somecompanies succeeded while others grew for a short timeand then stagnated and eventually failed Nord [9] identifies

Hindawi Publishing CorporationJournal of Industrial EngineeringVolume 2016 Article ID 1650863 16 pageshttpdxdoiorg10115520161650863

2 Journal of Industrial Engineering

The firm

Capacityacquisition

Orderfulfillment

Sales

Customerdemand

The market

Revenue

CapacityDeliverydelayutilisation

Customercontacts

Deliverydelay

Orders

Figure 1 Sectors of the market growth model (after Morecroft [12])

the capacity acquisition policy as a major factor in 52 ofthe cases of companies that failed within 5 years of start-up and he suggested that the use of different managementpolicies can either suppress or exacerbate the oscillatorygrowth No obvious reason could be found for failure otherthan the decisions taken by managers in response to marketchanges Morecroft [10ndash12] using a SystemDynamics modelhas linked the decision-making process and the strategydevelopment that is supported within the companyThe basicmodel of Morecroft intended to capture the essence of thedecision process is shown in Figure 1

Morecroftrsquos [12] model splits the problem of marketgrowth into two interactive regimes (a) the internal opera-tions of the firm and (b) the actions of the external marketforces Morecroftrsquos approach shows market forces externalto the company model and their interactions with thecompany model can be represented by a number of feedbackloops which describeMorecroftrsquos three key factors customercontacts delivery delays and the placement of orders

Although the model described here was intended forhigh-tech companies the challenges involved in capacityplanning aremore generic Bakke andHellberg [13] examinedthe problems in three different sectors maritime equipmentpaper manufacture and power production They identify anumber of similar problems in MRP operations across allthree sectors including instability caused by too much datain MPS systems neither load nor capacity being accuratelyknown and needing improved planning and reduction oflead times They also show capacity data exhibiting cyclicbehaviour very similar to the results shown herein later Dueto the nature of innovative products there is little historicaldata available for companies to use to forecast demandthe only methods available are comparison with lifecycles

of analogous products or the application of the predictivemethods pioneered by Bass [14] and Bass et al [15]

In view of the risks to the large amount of capital investedand the time factors involved manufacturers normally takea very cautious approach to building up capacity It isof particular importance in supply chain design that thedecisions regarding supply chain capacity and the policy ofcapacity increases or decreases are as efficient as possibleThedecisions susceptibilities can be classified into three broadareas

(1) capacity levels that do notmeet the full actual demandleading to nonavailability of products loss of revenueand market share

(2) delays in acquiring new capacity that involve consid-erable risk and may result in loss of both a marketopportunity and invested capital

(3) excess capacity that results in low plant utilisation andties up capital leading to low return on investment

Wild [16] defines capacity management as the cost effectivematching of capacity to demand and states that ldquomanagersmust consider current capacity and the required futurecapacity and the costs in implementing decisionsrdquo for anyproposed capacity change

Akkermans et al [17] have suggested that plant capacityspecification is a one-time decision This stance is notnormally the real world experience of most manufacturingcompanies since because of technological developments theyoften face the combined pressures of a decreasing product lifecycle shorter times to market and a cost-driven reliance onoutsourcing all of which require frequent changes in capacityto remain competitive

Journal of Industrial Engineering 3

Karrabuk and Wu [18] examined the capacity planningstrategy in the semiconductor industry claiming a near opti-mal investment policy which reconciled marketing andman-ufacturingWu et al [19] reviewed the literature onmanagingcapacity in high-tech industries with an emphasis on con-ventional inventory strategy choices such as the Newsvendor(ldquoNewsboyrdquo) models and multiperiod models with capacityadjustments The tendency to optimise investment basedon uncertain incentives results in difficult choices in rapidmarket changes The authors above applied the methods tosemiconductor wafer production An SD model was used byAdl and Parvizian [20] to investigate food production Theirwork is showing some cyclic capacity variation similar to thatobtained here

The factors underlying financial reasons for investmentare not well behaved continuous linear functions and thekey financial decisions in a company are normally madeonly when the strategic case for investment or disinvestmentis very clear cut (Ceryan and Koren [21]) Usually suchdecisions are strictly dependent on current and short rangepredicted sales that is short range strategic planning

The correct timing of an indicated capacity expansionis therefore vital This paper describes an implementationof Stermanrsquos [4] model itself based on Forresterrsquos original[8] proposal for modelling market growth This is comparedto an APVIOBPCS model (White and Censlive [22]) usinga modified control system which allows capacity to beincreased after a deliberation time using different decisionprotocols Sterman was interested in modelling ldquohigh-techrdquocompanies with their attendant dependence on technologyIn this case the products are usually innovative with fewcompetitors and companies must rely on their own dynamicsfor success or failure Either they sell their products or thecustomers have nothing Capacity acquisition decisions werefound to be the key strategy that dominated the success orfailure of these firms

The purpose of this paper is to investigate an improvedmodel of capacity acquisition developed by incorporatingrate of change of demand effects and simplifying the criteriafor decisions thus enabling an earlier intervention Thisapproach derives from Stermanrsquos observation that managersare unable to effectively detect rates of change of demand forlong lead times

We will show that a linear control based model of aproduction system combined with a nonlinear inventorysubsystem is able to represent the average behaviour of thesystem capacity and using Proportional Integral andDeriva-tive (PID) control improves the modelrsquos overall performancereducing the oscillatory behaviour of the Sterman model

2 Review

We now review relevant work on capacity management byother researchers especially concentrating on System Dy-namics (SD) models outlying their principal conclusionsModelling the behaviour of systems including supply chaineffects has traditionally used SD methods based on the workof Forrester [23] (Angerhofer and Angelides [24]) System

Dynamics models are widely used in modelling businessprocesses and are chosen for their capability to representsthe effects of physical flows as well as information flows inimplementing the respective time delays of the variables InSystemDynamicsmodelling it is important to understand thestructure of the interconnection between elements formingthe model because this dictates the behaviour of the modelIn systemsmodels the structure is interconnected by feedbackloops one ormore of whichwill be dominant and dictate howthe whole system responds to disturbances It is importantalso to realise that most SD modellers incorporate intotheir models ldquoreal worldrdquo data from one or more relevantcompanies in the form of nonlinear lookup tables so thatwhile themodels are supported by industry specific data theirusefulness is limited in any general applications outside theparticular systems studied

Capacitymodelling results reported in the literature suchas Suryani [25] can deal with strategic issues (with which weare concerned here) or with the more immediate localisedproduction control issues These problems are related to thetimescale of the planning exercise (Sterman [4]) Rajagopalanand Swaminathan [26] argue that the increase in productvariety may not result in excessive inventory or a substantialincrease in setting up times or an increase in costs due to theeffects of adding capacity to cope with the variety Andersonet al [27] use a System Dynamics (SD) model of a supplychainTheir results show that any tendency to impose systemwide targets increases variance in both demand and backlogThey confirm the commercial correctness of establishing anyconstraining backlog service points to be as near as possibleto the end use customer

As Sterman et al [28] suggest ldquoif firmswere well informedand could forecast accurately capacity would match orderswell (at least on average) Alternatively even if forecastingability were poor capacity would match demand if it couldbe adjusted rapidly and at low costrdquo One significant paperdealing with strategic problems is that of Yuan and Ashayeri[29] Their paper uses Stermanrsquos work and develops a controlsystems model with costing included Their model uses allthe functions used by Sterman and is hence nonlineartheir results show that the success of a supply chain isdirectly dependant on the intercompany cooperation and onthe delays in the system generated by the chain structureKamath and Roy [30] have investigated a comprehensiveSystem Dynamics model of capacity augmentation for shortproduct lifecycles finding that the loop dominance of thecoupling between the order and production outweighs theeffects of delivery delay on the dynamics of capacity growthVlachos et al [31] have shown that for production systemswhere remanufacturingreuse is present optimum responseis obtained when the review period is short that is less thanthe system time delays

The second class of problems pursued in the currentliterature (Duffie et al [32]) is concerned with effects inreconfigurable flexible plant for example Wiendahl andBreithaupt [33] applied control theory to the problem ofproduction control and devised the current methods ofldquologistic curvesrdquo and the ldquofunnel modelrdquo invoked by Nyhuis[34] to set up closed loop control of a PPCAsi andUlsoy [35]

4 Journal of Industrial Engineering

analysed capacitymanagement for a reconfigurablemanufac-turing systemusing stochasticmarket demand and developedsolutions to reduce delays in varying capacity Son et al [36]examined the costs in line balancing reconfigurable systemswith scalability Several of these authors have used PID(Proportional Integral and Derivative control) to improvethe system response PID control was proposed for supplychain use by several authors including Sharp and Henry [37]Towill and Yoon [38] and White [39]

Orcun et al [40] used System Dynamics models tocompare the effect of various clearing functions for capacitymodels on the production planning process A significantfinding was that the fixed lead time assumption fails togive accurate representation of the process at high capacityutilisation levels Elmasry et al [41] have used SD models toinvestigate scalable capacity manufacturing systems and theyfound the existence of critical conditions relative to systembreakdownThe role of control systems analysis in this type ofproblem is therefore long established and can produce usefulgeneral results

Investigations were undertaken by Georgiadis and col-leagues at the University of Thessaloniki using SD to modela range of closed loop supply chains which included aremanufacturing component (Georgiadis et al [42] Vlachoset al [31] Georgiadis and Politou [43] Georgiadis [44]and Georgiadis and Athanasiou [45]) The earliest of thesepapers shows the effect of changes in product lifecycle onthe overall performance of the process It is claimed thatfor their model the ldquooptimal parameters are insensitive tothe product demand levelrdquo The paper by Vlachos et al [31]examined the use of various ldquogreenrdquo strategies based onmeasuring the economic performance obtained by varyingthe amount of recycled materials Drum-Buffer-Rope pro-duction planning and control approach using an assumedldquonormally distributed demandwas investigated and indicatedinsensitivity of performance measures of manufacturing tochanges in control parametersrdquo Georgiadis [44] investigatedthe use of SD models in the paper industry to observe howrecycling strategies could maximise profitability

Georgiadis and Athanasiou [45] also cite evidence thatovercapacity in the US helicopter manufacturing industryappeared to reduce levels of technical innovation

Cannella et al [46] examined a capacity constrained sup-ply chain of 4 echelons with capacities at 6 different valuesfinding that the strategic implications required the elimina-tion of information distortion tomatch the supply to demandThe ultimate problem is to match the costs of investment innew capacity to prospective profits as the work of Ceryan andKoren [21] indicates

All the above cited papers indicated that the observedresponses of the models developed showed the presence ofcyclical capacity variation

3 Sterman Models

This section will introduce the model created by Stermanand its limitations and explain the basic equations used inthe modelTheMATLABSimulink version of that model

used here is described together with sample responses forcomparison

Stermanrsquos [4] model of a single firm competing in anunlimited market is shown in Figure 2 and was derived fromForresterrsquos [8] model of market growth Both Nord [9] andPacker [47] used similar models That the models could berelevant to various industries was shown by Leihr et al [48]who applied a similar model to the business cycles in theairline market producing similar oscillations that we findlater The Sterman model was used to test the theories ofbounded rationality [11] in an attempt to determine whymostnew companies fail Some companies grow and then stagnatewhile others suffer periodic crisis with a small number thatgrow and prosperThe SDmodel was devised to examine howbounded rational decisions could produce failure In morerecent times the early problems reported from the analysisof the financial state of Amazon were due to lack of availablewarehouse capacity

This model based on the analysis of Forrester and More-croft assumes that the firm manufactures high-tech productsas a build-to-order system It was not based on one companybut it included most of the representational features of suchcompanies while being as simple as possible However itincludes data derived from averaging a number of responsesto critical questions The system model shown in Figure 2contains three key variables states sales force and backlogand recent revenue There are three loops incorporatingfeedback with delays due to reporting and delivery Ordersare accumulated as a backlog until they have been producedand shippedThe actual delivery delay basically the residencetime in the backlog is the ratio of backlog to the currentshipment rateThe ratio ldquobook-to-billrdquo [order book = backloglevel billed = shipped and paid for] is a typical managementmeasure of the health of companies If this ratio is greaterthan unity then the company is growing insofar as theorder level continues to increase and hence an increase inproduction capacity is justifiable Desired production rate inthe model depends on the backlog but also on the normalor average value for the delivery delay For local managerscapacity is given by the available machinery at a particulartime and the decision to change the capacity of the plantis taken by senior management in response to a perceptionthat the sales will exceed capacity by a sufficient amount atsome future date Operations managers can only respond todemand by increasing the local capacity utilisation Whendesired production is less than plant capacity managerssometimes prefer to run down the backlog rather than layoff skilled workers and have idle plant The formulation ofdesired capacity was designed to capture important aspectsof bounded rationality Forrester had observed that seniormanagers were very conservative about capital investmentbeing very reluctant to invest in newplant until theywere surethat new capacity would not be underutilised They did nottrust sales forecasts basing their decisions onmissed deliverydates (because these are actual events not forecasts) by whichtime it was often too late to recover that customer

The Simulink representation of Stermanrsquos model pre-sented here uses the relationships and equations with thevariables expressed as continuous functions of time for

Journal of Industrial Engineering 5

Sales force

Targetsales force

Cost per salesrepresentative

Salesbudget

Backlog

Order rate

Shipmentrate

Revenue

Price

Saleseffectiveness

Recentrevenue Change in

recentrevenue

Desiredproduction

Capacityutilisation

Capacity

+

Sales forceadjustment

time

+

+

++

+

+

++

Fraction ofrevenue to

sales

+

Revenuereporting

delay

Normaldelivery

delay

+

Sales forcenet hiring

rate+

+

Table forcapacity

utilisation

Switch forcapacity

constraint

Switch forendogenous

orders

Exogenousorder rate

Initialbacklog

Initialcapacity

R1

Sales growth

minus

minus

minus

minus

minus

Figure 2 Stermanrsquos SD model for high-tech company growth

example OR(119905) rather than discrete data Two cases areconsidered by Sterman one where the orders are generatedby the sales force whose numbers are governed by the successthey have and a second case where orders come from outsideonly (exogenous) The equations relating the problem aredescribed below Considering the continuous variable casewe can develop the following equations

The rate of change of the backlog LEVEL (BL) is thedifference between the order rate (OR) and the shipping rate(SR)

119889BL (119905)119889119905 = OR (119905) minus SR (119905)

DD (119905) = BLSR(119905)

(1)

Delivery Delay (DD) is the ratio of backlog to shipping rate

SR (119905) = CAP (CU 119905) (2)

Shipping rate is equal to the current capacity (CAP) multi-plied by the capacity utilisation (CU)

CU (119905) = 119891( DP (119905)CAP (119905)) (3)

Capacity utilisation is some function of the ratio of desiredproduction (DP) to capacity

DP (119905) = BL (119905)NDD (4)

Desired production is the ratio of backlog to normal deliverydelay (NDD)

CAP (119905) = smooth 3 (DCAP 119879cad) (5)

Capacity is the smoothed delay value of desired capacity(DCAP) with characteristic time constant 119879cad

DCAP (119905) = (CAP (119905)) (EEPDC) (6)

The desired capacity is equal to the current capacity multi-plied by the effect of expansion pressure on desired capacity(EEPDC)

EEPDC = 119891 (PEC) (7)

Effect of expansion pressure on desired capacity is a functionof the pressure to expand capacity (PEC)

PEC (119905) = DDPCcgdd (8)

The pressure to expand capacity is expressed by the ratio ofthe delivery delay perceived by the company (DDPC) to thecompany goal for delivery delay (cgdd)

DDPC (119905) = smooth (DD 119879cpdd) (9)

The delivery delay perceived by the company is a smoothedvalue of the delivery delay with a timescale of 119879cpdd

The mathematical performance of the system is dictatedby three differential equations In the Simulink representation

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

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2 Journal of Industrial Engineering

The firm

Capacityacquisition

Orderfulfillment

Sales

Customerdemand

The market

Revenue

CapacityDeliverydelayutilisation

Customercontacts

Deliverydelay

Orders

Figure 1 Sectors of the market growth model (after Morecroft [12])

the capacity acquisition policy as a major factor in 52 ofthe cases of companies that failed within 5 years of start-up and he suggested that the use of different managementpolicies can either suppress or exacerbate the oscillatorygrowth No obvious reason could be found for failure otherthan the decisions taken by managers in response to marketchanges Morecroft [10ndash12] using a SystemDynamics modelhas linked the decision-making process and the strategydevelopment that is supported within the companyThe basicmodel of Morecroft intended to capture the essence of thedecision process is shown in Figure 1

Morecroftrsquos [12] model splits the problem of marketgrowth into two interactive regimes (a) the internal opera-tions of the firm and (b) the actions of the external marketforces Morecroftrsquos approach shows market forces externalto the company model and their interactions with thecompany model can be represented by a number of feedbackloops which describeMorecroftrsquos three key factors customercontacts delivery delays and the placement of orders

Although the model described here was intended forhigh-tech companies the challenges involved in capacityplanning aremore generic Bakke andHellberg [13] examinedthe problems in three different sectors maritime equipmentpaper manufacture and power production They identify anumber of similar problems in MRP operations across allthree sectors including instability caused by too much datain MPS systems neither load nor capacity being accuratelyknown and needing improved planning and reduction oflead times They also show capacity data exhibiting cyclicbehaviour very similar to the results shown herein later Dueto the nature of innovative products there is little historicaldata available for companies to use to forecast demandthe only methods available are comparison with lifecycles

of analogous products or the application of the predictivemethods pioneered by Bass [14] and Bass et al [15]

In view of the risks to the large amount of capital investedand the time factors involved manufacturers normally takea very cautious approach to building up capacity It isof particular importance in supply chain design that thedecisions regarding supply chain capacity and the policy ofcapacity increases or decreases are as efficient as possibleThedecisions susceptibilities can be classified into three broadareas

(1) capacity levels that do notmeet the full actual demandleading to nonavailability of products loss of revenueand market share

(2) delays in acquiring new capacity that involve consid-erable risk and may result in loss of both a marketopportunity and invested capital

(3) excess capacity that results in low plant utilisation andties up capital leading to low return on investment

Wild [16] defines capacity management as the cost effectivematching of capacity to demand and states that ldquomanagersmust consider current capacity and the required futurecapacity and the costs in implementing decisionsrdquo for anyproposed capacity change

Akkermans et al [17] have suggested that plant capacityspecification is a one-time decision This stance is notnormally the real world experience of most manufacturingcompanies since because of technological developments theyoften face the combined pressures of a decreasing product lifecycle shorter times to market and a cost-driven reliance onoutsourcing all of which require frequent changes in capacityto remain competitive

Journal of Industrial Engineering 3

Karrabuk and Wu [18] examined the capacity planningstrategy in the semiconductor industry claiming a near opti-mal investment policy which reconciled marketing andman-ufacturingWu et al [19] reviewed the literature onmanagingcapacity in high-tech industries with an emphasis on con-ventional inventory strategy choices such as the Newsvendor(ldquoNewsboyrdquo) models and multiperiod models with capacityadjustments The tendency to optimise investment basedon uncertain incentives results in difficult choices in rapidmarket changes The authors above applied the methods tosemiconductor wafer production An SD model was used byAdl and Parvizian [20] to investigate food production Theirwork is showing some cyclic capacity variation similar to thatobtained here

The factors underlying financial reasons for investmentare not well behaved continuous linear functions and thekey financial decisions in a company are normally madeonly when the strategic case for investment or disinvestmentis very clear cut (Ceryan and Koren [21]) Usually suchdecisions are strictly dependent on current and short rangepredicted sales that is short range strategic planning

The correct timing of an indicated capacity expansionis therefore vital This paper describes an implementationof Stermanrsquos [4] model itself based on Forresterrsquos original[8] proposal for modelling market growth This is comparedto an APVIOBPCS model (White and Censlive [22]) usinga modified control system which allows capacity to beincreased after a deliberation time using different decisionprotocols Sterman was interested in modelling ldquohigh-techrdquocompanies with their attendant dependence on technologyIn this case the products are usually innovative with fewcompetitors and companies must rely on their own dynamicsfor success or failure Either they sell their products or thecustomers have nothing Capacity acquisition decisions werefound to be the key strategy that dominated the success orfailure of these firms

The purpose of this paper is to investigate an improvedmodel of capacity acquisition developed by incorporatingrate of change of demand effects and simplifying the criteriafor decisions thus enabling an earlier intervention Thisapproach derives from Stermanrsquos observation that managersare unable to effectively detect rates of change of demand forlong lead times

We will show that a linear control based model of aproduction system combined with a nonlinear inventorysubsystem is able to represent the average behaviour of thesystem capacity and using Proportional Integral andDeriva-tive (PID) control improves the modelrsquos overall performancereducing the oscillatory behaviour of the Sterman model

2 Review

We now review relevant work on capacity management byother researchers especially concentrating on System Dy-namics (SD) models outlying their principal conclusionsModelling the behaviour of systems including supply chaineffects has traditionally used SD methods based on the workof Forrester [23] (Angerhofer and Angelides [24]) System

Dynamics models are widely used in modelling businessprocesses and are chosen for their capability to representsthe effects of physical flows as well as information flows inimplementing the respective time delays of the variables InSystemDynamicsmodelling it is important to understand thestructure of the interconnection between elements formingthe model because this dictates the behaviour of the modelIn systemsmodels the structure is interconnected by feedbackloops one ormore of whichwill be dominant and dictate howthe whole system responds to disturbances It is importantalso to realise that most SD modellers incorporate intotheir models ldquoreal worldrdquo data from one or more relevantcompanies in the form of nonlinear lookup tables so thatwhile themodels are supported by industry specific data theirusefulness is limited in any general applications outside theparticular systems studied

Capacitymodelling results reported in the literature suchas Suryani [25] can deal with strategic issues (with which weare concerned here) or with the more immediate localisedproduction control issues These problems are related to thetimescale of the planning exercise (Sterman [4]) Rajagopalanand Swaminathan [26] argue that the increase in productvariety may not result in excessive inventory or a substantialincrease in setting up times or an increase in costs due to theeffects of adding capacity to cope with the variety Andersonet al [27] use a System Dynamics (SD) model of a supplychainTheir results show that any tendency to impose systemwide targets increases variance in both demand and backlogThey confirm the commercial correctness of establishing anyconstraining backlog service points to be as near as possibleto the end use customer

As Sterman et al [28] suggest ldquoif firmswere well informedand could forecast accurately capacity would match orderswell (at least on average) Alternatively even if forecastingability were poor capacity would match demand if it couldbe adjusted rapidly and at low costrdquo One significant paperdealing with strategic problems is that of Yuan and Ashayeri[29] Their paper uses Stermanrsquos work and develops a controlsystems model with costing included Their model uses allthe functions used by Sterman and is hence nonlineartheir results show that the success of a supply chain isdirectly dependant on the intercompany cooperation and onthe delays in the system generated by the chain structureKamath and Roy [30] have investigated a comprehensiveSystem Dynamics model of capacity augmentation for shortproduct lifecycles finding that the loop dominance of thecoupling between the order and production outweighs theeffects of delivery delay on the dynamics of capacity growthVlachos et al [31] have shown that for production systemswhere remanufacturingreuse is present optimum responseis obtained when the review period is short that is less thanthe system time delays

The second class of problems pursued in the currentliterature (Duffie et al [32]) is concerned with effects inreconfigurable flexible plant for example Wiendahl andBreithaupt [33] applied control theory to the problem ofproduction control and devised the current methods ofldquologistic curvesrdquo and the ldquofunnel modelrdquo invoked by Nyhuis[34] to set up closed loop control of a PPCAsi andUlsoy [35]

4 Journal of Industrial Engineering

analysed capacitymanagement for a reconfigurablemanufac-turing systemusing stochasticmarket demand and developedsolutions to reduce delays in varying capacity Son et al [36]examined the costs in line balancing reconfigurable systemswith scalability Several of these authors have used PID(Proportional Integral and Derivative control) to improvethe system response PID control was proposed for supplychain use by several authors including Sharp and Henry [37]Towill and Yoon [38] and White [39]

Orcun et al [40] used System Dynamics models tocompare the effect of various clearing functions for capacitymodels on the production planning process A significantfinding was that the fixed lead time assumption fails togive accurate representation of the process at high capacityutilisation levels Elmasry et al [41] have used SD models toinvestigate scalable capacity manufacturing systems and theyfound the existence of critical conditions relative to systembreakdownThe role of control systems analysis in this type ofproblem is therefore long established and can produce usefulgeneral results

Investigations were undertaken by Georgiadis and col-leagues at the University of Thessaloniki using SD to modela range of closed loop supply chains which included aremanufacturing component (Georgiadis et al [42] Vlachoset al [31] Georgiadis and Politou [43] Georgiadis [44]and Georgiadis and Athanasiou [45]) The earliest of thesepapers shows the effect of changes in product lifecycle onthe overall performance of the process It is claimed thatfor their model the ldquooptimal parameters are insensitive tothe product demand levelrdquo The paper by Vlachos et al [31]examined the use of various ldquogreenrdquo strategies based onmeasuring the economic performance obtained by varyingthe amount of recycled materials Drum-Buffer-Rope pro-duction planning and control approach using an assumedldquonormally distributed demandwas investigated and indicatedinsensitivity of performance measures of manufacturing tochanges in control parametersrdquo Georgiadis [44] investigatedthe use of SD models in the paper industry to observe howrecycling strategies could maximise profitability

Georgiadis and Athanasiou [45] also cite evidence thatovercapacity in the US helicopter manufacturing industryappeared to reduce levels of technical innovation

Cannella et al [46] examined a capacity constrained sup-ply chain of 4 echelons with capacities at 6 different valuesfinding that the strategic implications required the elimina-tion of information distortion tomatch the supply to demandThe ultimate problem is to match the costs of investment innew capacity to prospective profits as the work of Ceryan andKoren [21] indicates

All the above cited papers indicated that the observedresponses of the models developed showed the presence ofcyclical capacity variation

3 Sterman Models

This section will introduce the model created by Stermanand its limitations and explain the basic equations used inthe modelTheMATLABSimulink version of that model

used here is described together with sample responses forcomparison

Stermanrsquos [4] model of a single firm competing in anunlimited market is shown in Figure 2 and was derived fromForresterrsquos [8] model of market growth Both Nord [9] andPacker [47] used similar models That the models could berelevant to various industries was shown by Leihr et al [48]who applied a similar model to the business cycles in theairline market producing similar oscillations that we findlater The Sterman model was used to test the theories ofbounded rationality [11] in an attempt to determine whymostnew companies fail Some companies grow and then stagnatewhile others suffer periodic crisis with a small number thatgrow and prosperThe SDmodel was devised to examine howbounded rational decisions could produce failure In morerecent times the early problems reported from the analysisof the financial state of Amazon were due to lack of availablewarehouse capacity

This model based on the analysis of Forrester and More-croft assumes that the firm manufactures high-tech productsas a build-to-order system It was not based on one companybut it included most of the representational features of suchcompanies while being as simple as possible However itincludes data derived from averaging a number of responsesto critical questions The system model shown in Figure 2contains three key variables states sales force and backlogand recent revenue There are three loops incorporatingfeedback with delays due to reporting and delivery Ordersare accumulated as a backlog until they have been producedand shippedThe actual delivery delay basically the residencetime in the backlog is the ratio of backlog to the currentshipment rateThe ratio ldquobook-to-billrdquo [order book = backloglevel billed = shipped and paid for] is a typical managementmeasure of the health of companies If this ratio is greaterthan unity then the company is growing insofar as theorder level continues to increase and hence an increase inproduction capacity is justifiable Desired production rate inthe model depends on the backlog but also on the normalor average value for the delivery delay For local managerscapacity is given by the available machinery at a particulartime and the decision to change the capacity of the plantis taken by senior management in response to a perceptionthat the sales will exceed capacity by a sufficient amount atsome future date Operations managers can only respond todemand by increasing the local capacity utilisation Whendesired production is less than plant capacity managerssometimes prefer to run down the backlog rather than layoff skilled workers and have idle plant The formulation ofdesired capacity was designed to capture important aspectsof bounded rationality Forrester had observed that seniormanagers were very conservative about capital investmentbeing very reluctant to invest in newplant until theywere surethat new capacity would not be underutilised They did nottrust sales forecasts basing their decisions onmissed deliverydates (because these are actual events not forecasts) by whichtime it was often too late to recover that customer

The Simulink representation of Stermanrsquos model pre-sented here uses the relationships and equations with thevariables expressed as continuous functions of time for

Journal of Industrial Engineering 5

Sales force

Targetsales force

Cost per salesrepresentative

Salesbudget

Backlog

Order rate

Shipmentrate

Revenue

Price

Saleseffectiveness

Recentrevenue Change in

recentrevenue

Desiredproduction

Capacityutilisation

Capacity

+

Sales forceadjustment

time

+

+

++

+

+

++

Fraction ofrevenue to

sales

+

Revenuereporting

delay

Normaldelivery

delay

+

Sales forcenet hiring

rate+

+

Table forcapacity

utilisation

Switch forcapacity

constraint

Switch forendogenous

orders

Exogenousorder rate

Initialbacklog

Initialcapacity

R1

Sales growth

minus

minus

minus

minus

minus

Figure 2 Stermanrsquos SD model for high-tech company growth

example OR(119905) rather than discrete data Two cases areconsidered by Sterman one where the orders are generatedby the sales force whose numbers are governed by the successthey have and a second case where orders come from outsideonly (exogenous) The equations relating the problem aredescribed below Considering the continuous variable casewe can develop the following equations

The rate of change of the backlog LEVEL (BL) is thedifference between the order rate (OR) and the shipping rate(SR)

119889BL (119905)119889119905 = OR (119905) minus SR (119905)

DD (119905) = BLSR(119905)

(1)

Delivery Delay (DD) is the ratio of backlog to shipping rate

SR (119905) = CAP (CU 119905) (2)

Shipping rate is equal to the current capacity (CAP) multi-plied by the capacity utilisation (CU)

CU (119905) = 119891( DP (119905)CAP (119905)) (3)

Capacity utilisation is some function of the ratio of desiredproduction (DP) to capacity

DP (119905) = BL (119905)NDD (4)

Desired production is the ratio of backlog to normal deliverydelay (NDD)

CAP (119905) = smooth 3 (DCAP 119879cad) (5)

Capacity is the smoothed delay value of desired capacity(DCAP) with characteristic time constant 119879cad

DCAP (119905) = (CAP (119905)) (EEPDC) (6)

The desired capacity is equal to the current capacity multi-plied by the effect of expansion pressure on desired capacity(EEPDC)

EEPDC = 119891 (PEC) (7)

Effect of expansion pressure on desired capacity is a functionof the pressure to expand capacity (PEC)

PEC (119905) = DDPCcgdd (8)

The pressure to expand capacity is expressed by the ratio ofthe delivery delay perceived by the company (DDPC) to thecompany goal for delivery delay (cgdd)

DDPC (119905) = smooth (DD 119879cpdd) (9)

The delivery delay perceived by the company is a smoothedvalue of the delivery delay with a timescale of 119879cpdd

The mathematical performance of the system is dictatedby three differential equations In the Simulink representation

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 3

Karrabuk and Wu [18] examined the capacity planningstrategy in the semiconductor industry claiming a near opti-mal investment policy which reconciled marketing andman-ufacturingWu et al [19] reviewed the literature onmanagingcapacity in high-tech industries with an emphasis on con-ventional inventory strategy choices such as the Newsvendor(ldquoNewsboyrdquo) models and multiperiod models with capacityadjustments The tendency to optimise investment basedon uncertain incentives results in difficult choices in rapidmarket changes The authors above applied the methods tosemiconductor wafer production An SD model was used byAdl and Parvizian [20] to investigate food production Theirwork is showing some cyclic capacity variation similar to thatobtained here

The factors underlying financial reasons for investmentare not well behaved continuous linear functions and thekey financial decisions in a company are normally madeonly when the strategic case for investment or disinvestmentis very clear cut (Ceryan and Koren [21]) Usually suchdecisions are strictly dependent on current and short rangepredicted sales that is short range strategic planning

The correct timing of an indicated capacity expansionis therefore vital This paper describes an implementationof Stermanrsquos [4] model itself based on Forresterrsquos original[8] proposal for modelling market growth This is comparedto an APVIOBPCS model (White and Censlive [22]) usinga modified control system which allows capacity to beincreased after a deliberation time using different decisionprotocols Sterman was interested in modelling ldquohigh-techrdquocompanies with their attendant dependence on technologyIn this case the products are usually innovative with fewcompetitors and companies must rely on their own dynamicsfor success or failure Either they sell their products or thecustomers have nothing Capacity acquisition decisions werefound to be the key strategy that dominated the success orfailure of these firms

The purpose of this paper is to investigate an improvedmodel of capacity acquisition developed by incorporatingrate of change of demand effects and simplifying the criteriafor decisions thus enabling an earlier intervention Thisapproach derives from Stermanrsquos observation that managersare unable to effectively detect rates of change of demand forlong lead times

We will show that a linear control based model of aproduction system combined with a nonlinear inventorysubsystem is able to represent the average behaviour of thesystem capacity and using Proportional Integral andDeriva-tive (PID) control improves the modelrsquos overall performancereducing the oscillatory behaviour of the Sterman model

2 Review

We now review relevant work on capacity management byother researchers especially concentrating on System Dy-namics (SD) models outlying their principal conclusionsModelling the behaviour of systems including supply chaineffects has traditionally used SD methods based on the workof Forrester [23] (Angerhofer and Angelides [24]) System

Dynamics models are widely used in modelling businessprocesses and are chosen for their capability to representsthe effects of physical flows as well as information flows inimplementing the respective time delays of the variables InSystemDynamicsmodelling it is important to understand thestructure of the interconnection between elements formingthe model because this dictates the behaviour of the modelIn systemsmodels the structure is interconnected by feedbackloops one ormore of whichwill be dominant and dictate howthe whole system responds to disturbances It is importantalso to realise that most SD modellers incorporate intotheir models ldquoreal worldrdquo data from one or more relevantcompanies in the form of nonlinear lookup tables so thatwhile themodels are supported by industry specific data theirusefulness is limited in any general applications outside theparticular systems studied

Capacitymodelling results reported in the literature suchas Suryani [25] can deal with strategic issues (with which weare concerned here) or with the more immediate localisedproduction control issues These problems are related to thetimescale of the planning exercise (Sterman [4]) Rajagopalanand Swaminathan [26] argue that the increase in productvariety may not result in excessive inventory or a substantialincrease in setting up times or an increase in costs due to theeffects of adding capacity to cope with the variety Andersonet al [27] use a System Dynamics (SD) model of a supplychainTheir results show that any tendency to impose systemwide targets increases variance in both demand and backlogThey confirm the commercial correctness of establishing anyconstraining backlog service points to be as near as possibleto the end use customer

As Sterman et al [28] suggest ldquoif firmswere well informedand could forecast accurately capacity would match orderswell (at least on average) Alternatively even if forecastingability were poor capacity would match demand if it couldbe adjusted rapidly and at low costrdquo One significant paperdealing with strategic problems is that of Yuan and Ashayeri[29] Their paper uses Stermanrsquos work and develops a controlsystems model with costing included Their model uses allthe functions used by Sterman and is hence nonlineartheir results show that the success of a supply chain isdirectly dependant on the intercompany cooperation and onthe delays in the system generated by the chain structureKamath and Roy [30] have investigated a comprehensiveSystem Dynamics model of capacity augmentation for shortproduct lifecycles finding that the loop dominance of thecoupling between the order and production outweighs theeffects of delivery delay on the dynamics of capacity growthVlachos et al [31] have shown that for production systemswhere remanufacturingreuse is present optimum responseis obtained when the review period is short that is less thanthe system time delays

The second class of problems pursued in the currentliterature (Duffie et al [32]) is concerned with effects inreconfigurable flexible plant for example Wiendahl andBreithaupt [33] applied control theory to the problem ofproduction control and devised the current methods ofldquologistic curvesrdquo and the ldquofunnel modelrdquo invoked by Nyhuis[34] to set up closed loop control of a PPCAsi andUlsoy [35]

4 Journal of Industrial Engineering

analysed capacitymanagement for a reconfigurablemanufac-turing systemusing stochasticmarket demand and developedsolutions to reduce delays in varying capacity Son et al [36]examined the costs in line balancing reconfigurable systemswith scalability Several of these authors have used PID(Proportional Integral and Derivative control) to improvethe system response PID control was proposed for supplychain use by several authors including Sharp and Henry [37]Towill and Yoon [38] and White [39]

Orcun et al [40] used System Dynamics models tocompare the effect of various clearing functions for capacitymodels on the production planning process A significantfinding was that the fixed lead time assumption fails togive accurate representation of the process at high capacityutilisation levels Elmasry et al [41] have used SD models toinvestigate scalable capacity manufacturing systems and theyfound the existence of critical conditions relative to systembreakdownThe role of control systems analysis in this type ofproblem is therefore long established and can produce usefulgeneral results

Investigations were undertaken by Georgiadis and col-leagues at the University of Thessaloniki using SD to modela range of closed loop supply chains which included aremanufacturing component (Georgiadis et al [42] Vlachoset al [31] Georgiadis and Politou [43] Georgiadis [44]and Georgiadis and Athanasiou [45]) The earliest of thesepapers shows the effect of changes in product lifecycle onthe overall performance of the process It is claimed thatfor their model the ldquooptimal parameters are insensitive tothe product demand levelrdquo The paper by Vlachos et al [31]examined the use of various ldquogreenrdquo strategies based onmeasuring the economic performance obtained by varyingthe amount of recycled materials Drum-Buffer-Rope pro-duction planning and control approach using an assumedldquonormally distributed demandwas investigated and indicatedinsensitivity of performance measures of manufacturing tochanges in control parametersrdquo Georgiadis [44] investigatedthe use of SD models in the paper industry to observe howrecycling strategies could maximise profitability

Georgiadis and Athanasiou [45] also cite evidence thatovercapacity in the US helicopter manufacturing industryappeared to reduce levels of technical innovation

Cannella et al [46] examined a capacity constrained sup-ply chain of 4 echelons with capacities at 6 different valuesfinding that the strategic implications required the elimina-tion of information distortion tomatch the supply to demandThe ultimate problem is to match the costs of investment innew capacity to prospective profits as the work of Ceryan andKoren [21] indicates

All the above cited papers indicated that the observedresponses of the models developed showed the presence ofcyclical capacity variation

3 Sterman Models

This section will introduce the model created by Stermanand its limitations and explain the basic equations used inthe modelTheMATLABSimulink version of that model

used here is described together with sample responses forcomparison

Stermanrsquos [4] model of a single firm competing in anunlimited market is shown in Figure 2 and was derived fromForresterrsquos [8] model of market growth Both Nord [9] andPacker [47] used similar models That the models could berelevant to various industries was shown by Leihr et al [48]who applied a similar model to the business cycles in theairline market producing similar oscillations that we findlater The Sterman model was used to test the theories ofbounded rationality [11] in an attempt to determine whymostnew companies fail Some companies grow and then stagnatewhile others suffer periodic crisis with a small number thatgrow and prosperThe SDmodel was devised to examine howbounded rational decisions could produce failure In morerecent times the early problems reported from the analysisof the financial state of Amazon were due to lack of availablewarehouse capacity

This model based on the analysis of Forrester and More-croft assumes that the firm manufactures high-tech productsas a build-to-order system It was not based on one companybut it included most of the representational features of suchcompanies while being as simple as possible However itincludes data derived from averaging a number of responsesto critical questions The system model shown in Figure 2contains three key variables states sales force and backlogand recent revenue There are three loops incorporatingfeedback with delays due to reporting and delivery Ordersare accumulated as a backlog until they have been producedand shippedThe actual delivery delay basically the residencetime in the backlog is the ratio of backlog to the currentshipment rateThe ratio ldquobook-to-billrdquo [order book = backloglevel billed = shipped and paid for] is a typical managementmeasure of the health of companies If this ratio is greaterthan unity then the company is growing insofar as theorder level continues to increase and hence an increase inproduction capacity is justifiable Desired production rate inthe model depends on the backlog but also on the normalor average value for the delivery delay For local managerscapacity is given by the available machinery at a particulartime and the decision to change the capacity of the plantis taken by senior management in response to a perceptionthat the sales will exceed capacity by a sufficient amount atsome future date Operations managers can only respond todemand by increasing the local capacity utilisation Whendesired production is less than plant capacity managerssometimes prefer to run down the backlog rather than layoff skilled workers and have idle plant The formulation ofdesired capacity was designed to capture important aspectsof bounded rationality Forrester had observed that seniormanagers were very conservative about capital investmentbeing very reluctant to invest in newplant until theywere surethat new capacity would not be underutilised They did nottrust sales forecasts basing their decisions onmissed deliverydates (because these are actual events not forecasts) by whichtime it was often too late to recover that customer

The Simulink representation of Stermanrsquos model pre-sented here uses the relationships and equations with thevariables expressed as continuous functions of time for

Journal of Industrial Engineering 5

Sales force

Targetsales force

Cost per salesrepresentative

Salesbudget

Backlog

Order rate

Shipmentrate

Revenue

Price

Saleseffectiveness

Recentrevenue Change in

recentrevenue

Desiredproduction

Capacityutilisation

Capacity

+

Sales forceadjustment

time

+

+

++

+

+

++

Fraction ofrevenue to

sales

+

Revenuereporting

delay

Normaldelivery

delay

+

Sales forcenet hiring

rate+

+

Table forcapacity

utilisation

Switch forcapacity

constraint

Switch forendogenous

orders

Exogenousorder rate

Initialbacklog

Initialcapacity

R1

Sales growth

minus

minus

minus

minus

minus

Figure 2 Stermanrsquos SD model for high-tech company growth

example OR(119905) rather than discrete data Two cases areconsidered by Sterman one where the orders are generatedby the sales force whose numbers are governed by the successthey have and a second case where orders come from outsideonly (exogenous) The equations relating the problem aredescribed below Considering the continuous variable casewe can develop the following equations

The rate of change of the backlog LEVEL (BL) is thedifference between the order rate (OR) and the shipping rate(SR)

119889BL (119905)119889119905 = OR (119905) minus SR (119905)

DD (119905) = BLSR(119905)

(1)

Delivery Delay (DD) is the ratio of backlog to shipping rate

SR (119905) = CAP (CU 119905) (2)

Shipping rate is equal to the current capacity (CAP) multi-plied by the capacity utilisation (CU)

CU (119905) = 119891( DP (119905)CAP (119905)) (3)

Capacity utilisation is some function of the ratio of desiredproduction (DP) to capacity

DP (119905) = BL (119905)NDD (4)

Desired production is the ratio of backlog to normal deliverydelay (NDD)

CAP (119905) = smooth 3 (DCAP 119879cad) (5)

Capacity is the smoothed delay value of desired capacity(DCAP) with characteristic time constant 119879cad

DCAP (119905) = (CAP (119905)) (EEPDC) (6)

The desired capacity is equal to the current capacity multi-plied by the effect of expansion pressure on desired capacity(EEPDC)

EEPDC = 119891 (PEC) (7)

Effect of expansion pressure on desired capacity is a functionof the pressure to expand capacity (PEC)

PEC (119905) = DDPCcgdd (8)

The pressure to expand capacity is expressed by the ratio ofthe delivery delay perceived by the company (DDPC) to thecompany goal for delivery delay (cgdd)

DDPC (119905) = smooth (DD 119879cpdd) (9)

The delivery delay perceived by the company is a smoothedvalue of the delivery delay with a timescale of 119879cpdd

The mathematical performance of the system is dictatedby three differential equations In the Simulink representation

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

4 Journal of Industrial Engineering

analysed capacitymanagement for a reconfigurablemanufac-turing systemusing stochasticmarket demand and developedsolutions to reduce delays in varying capacity Son et al [36]examined the costs in line balancing reconfigurable systemswith scalability Several of these authors have used PID(Proportional Integral and Derivative control) to improvethe system response PID control was proposed for supplychain use by several authors including Sharp and Henry [37]Towill and Yoon [38] and White [39]

Orcun et al [40] used System Dynamics models tocompare the effect of various clearing functions for capacitymodels on the production planning process A significantfinding was that the fixed lead time assumption fails togive accurate representation of the process at high capacityutilisation levels Elmasry et al [41] have used SD models toinvestigate scalable capacity manufacturing systems and theyfound the existence of critical conditions relative to systembreakdownThe role of control systems analysis in this type ofproblem is therefore long established and can produce usefulgeneral results

Investigations were undertaken by Georgiadis and col-leagues at the University of Thessaloniki using SD to modela range of closed loop supply chains which included aremanufacturing component (Georgiadis et al [42] Vlachoset al [31] Georgiadis and Politou [43] Georgiadis [44]and Georgiadis and Athanasiou [45]) The earliest of thesepapers shows the effect of changes in product lifecycle onthe overall performance of the process It is claimed thatfor their model the ldquooptimal parameters are insensitive tothe product demand levelrdquo The paper by Vlachos et al [31]examined the use of various ldquogreenrdquo strategies based onmeasuring the economic performance obtained by varyingthe amount of recycled materials Drum-Buffer-Rope pro-duction planning and control approach using an assumedldquonormally distributed demandwas investigated and indicatedinsensitivity of performance measures of manufacturing tochanges in control parametersrdquo Georgiadis [44] investigatedthe use of SD models in the paper industry to observe howrecycling strategies could maximise profitability

Georgiadis and Athanasiou [45] also cite evidence thatovercapacity in the US helicopter manufacturing industryappeared to reduce levels of technical innovation

Cannella et al [46] examined a capacity constrained sup-ply chain of 4 echelons with capacities at 6 different valuesfinding that the strategic implications required the elimina-tion of information distortion tomatch the supply to demandThe ultimate problem is to match the costs of investment innew capacity to prospective profits as the work of Ceryan andKoren [21] indicates

All the above cited papers indicated that the observedresponses of the models developed showed the presence ofcyclical capacity variation

3 Sterman Models

This section will introduce the model created by Stermanand its limitations and explain the basic equations used inthe modelTheMATLABSimulink version of that model

used here is described together with sample responses forcomparison

Stermanrsquos [4] model of a single firm competing in anunlimited market is shown in Figure 2 and was derived fromForresterrsquos [8] model of market growth Both Nord [9] andPacker [47] used similar models That the models could berelevant to various industries was shown by Leihr et al [48]who applied a similar model to the business cycles in theairline market producing similar oscillations that we findlater The Sterman model was used to test the theories ofbounded rationality [11] in an attempt to determine whymostnew companies fail Some companies grow and then stagnatewhile others suffer periodic crisis with a small number thatgrow and prosperThe SDmodel was devised to examine howbounded rational decisions could produce failure In morerecent times the early problems reported from the analysisof the financial state of Amazon were due to lack of availablewarehouse capacity

This model based on the analysis of Forrester and More-croft assumes that the firm manufactures high-tech productsas a build-to-order system It was not based on one companybut it included most of the representational features of suchcompanies while being as simple as possible However itincludes data derived from averaging a number of responsesto critical questions The system model shown in Figure 2contains three key variables states sales force and backlogand recent revenue There are three loops incorporatingfeedback with delays due to reporting and delivery Ordersare accumulated as a backlog until they have been producedand shippedThe actual delivery delay basically the residencetime in the backlog is the ratio of backlog to the currentshipment rateThe ratio ldquobook-to-billrdquo [order book = backloglevel billed = shipped and paid for] is a typical managementmeasure of the health of companies If this ratio is greaterthan unity then the company is growing insofar as theorder level continues to increase and hence an increase inproduction capacity is justifiable Desired production rate inthe model depends on the backlog but also on the normalor average value for the delivery delay For local managerscapacity is given by the available machinery at a particulartime and the decision to change the capacity of the plantis taken by senior management in response to a perceptionthat the sales will exceed capacity by a sufficient amount atsome future date Operations managers can only respond todemand by increasing the local capacity utilisation Whendesired production is less than plant capacity managerssometimes prefer to run down the backlog rather than layoff skilled workers and have idle plant The formulation ofdesired capacity was designed to capture important aspectsof bounded rationality Forrester had observed that seniormanagers were very conservative about capital investmentbeing very reluctant to invest in newplant until theywere surethat new capacity would not be underutilised They did nottrust sales forecasts basing their decisions onmissed deliverydates (because these are actual events not forecasts) by whichtime it was often too late to recover that customer

The Simulink representation of Stermanrsquos model pre-sented here uses the relationships and equations with thevariables expressed as continuous functions of time for

Journal of Industrial Engineering 5

Sales force

Targetsales force

Cost per salesrepresentative

Salesbudget

Backlog

Order rate

Shipmentrate

Revenue

Price

Saleseffectiveness

Recentrevenue Change in

recentrevenue

Desiredproduction

Capacityutilisation

Capacity

+

Sales forceadjustment

time

+

+

++

+

+

++

Fraction ofrevenue to

sales

+

Revenuereporting

delay

Normaldelivery

delay

+

Sales forcenet hiring

rate+

+

Table forcapacity

utilisation

Switch forcapacity

constraint

Switch forendogenous

orders

Exogenousorder rate

Initialbacklog

Initialcapacity

R1

Sales growth

minus

minus

minus

minus

minus

Figure 2 Stermanrsquos SD model for high-tech company growth

example OR(119905) rather than discrete data Two cases areconsidered by Sterman one where the orders are generatedby the sales force whose numbers are governed by the successthey have and a second case where orders come from outsideonly (exogenous) The equations relating the problem aredescribed below Considering the continuous variable casewe can develop the following equations

The rate of change of the backlog LEVEL (BL) is thedifference between the order rate (OR) and the shipping rate(SR)

119889BL (119905)119889119905 = OR (119905) minus SR (119905)

DD (119905) = BLSR(119905)

(1)

Delivery Delay (DD) is the ratio of backlog to shipping rate

SR (119905) = CAP (CU 119905) (2)

Shipping rate is equal to the current capacity (CAP) multi-plied by the capacity utilisation (CU)

CU (119905) = 119891( DP (119905)CAP (119905)) (3)

Capacity utilisation is some function of the ratio of desiredproduction (DP) to capacity

DP (119905) = BL (119905)NDD (4)

Desired production is the ratio of backlog to normal deliverydelay (NDD)

CAP (119905) = smooth 3 (DCAP 119879cad) (5)

Capacity is the smoothed delay value of desired capacity(DCAP) with characteristic time constant 119879cad

DCAP (119905) = (CAP (119905)) (EEPDC) (6)

The desired capacity is equal to the current capacity multi-plied by the effect of expansion pressure on desired capacity(EEPDC)

EEPDC = 119891 (PEC) (7)

Effect of expansion pressure on desired capacity is a functionof the pressure to expand capacity (PEC)

PEC (119905) = DDPCcgdd (8)

The pressure to expand capacity is expressed by the ratio ofthe delivery delay perceived by the company (DDPC) to thecompany goal for delivery delay (cgdd)

DDPC (119905) = smooth (DD 119879cpdd) (9)

The delivery delay perceived by the company is a smoothedvalue of the delivery delay with a timescale of 119879cpdd

The mathematical performance of the system is dictatedby three differential equations In the Simulink representation

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

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Submit your manuscripts athttpwwwhindawicom

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DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 5

Sales force

Targetsales force

Cost per salesrepresentative

Salesbudget

Backlog

Order rate

Shipmentrate

Revenue

Price

Saleseffectiveness

Recentrevenue Change in

recentrevenue

Desiredproduction

Capacityutilisation

Capacity

+

Sales forceadjustment

time

+

+

++

+

+

++

Fraction ofrevenue to

sales

+

Revenuereporting

delay

Normaldelivery

delay

+

Sales forcenet hiring

rate+

+

Table forcapacity

utilisation

Switch forcapacity

constraint

Switch forendogenous

orders

Exogenousorder rate

Initialbacklog

Initialcapacity

R1

Sales growth

minus

minus

minus

minus

minus

Figure 2 Stermanrsquos SD model for high-tech company growth

example OR(119905) rather than discrete data Two cases areconsidered by Sterman one where the orders are generatedby the sales force whose numbers are governed by the successthey have and a second case where orders come from outsideonly (exogenous) The equations relating the problem aredescribed below Considering the continuous variable casewe can develop the following equations

The rate of change of the backlog LEVEL (BL) is thedifference between the order rate (OR) and the shipping rate(SR)

119889BL (119905)119889119905 = OR (119905) minus SR (119905)

DD (119905) = BLSR(119905)

(1)

Delivery Delay (DD) is the ratio of backlog to shipping rate

SR (119905) = CAP (CU 119905) (2)

Shipping rate is equal to the current capacity (CAP) multi-plied by the capacity utilisation (CU)

CU (119905) = 119891( DP (119905)CAP (119905)) (3)

Capacity utilisation is some function of the ratio of desiredproduction (DP) to capacity

DP (119905) = BL (119905)NDD (4)

Desired production is the ratio of backlog to normal deliverydelay (NDD)

CAP (119905) = smooth 3 (DCAP 119879cad) (5)

Capacity is the smoothed delay value of desired capacity(DCAP) with characteristic time constant 119879cad

DCAP (119905) = (CAP (119905)) (EEPDC) (6)

The desired capacity is equal to the current capacity multi-plied by the effect of expansion pressure on desired capacity(EEPDC)

EEPDC = 119891 (PEC) (7)

Effect of expansion pressure on desired capacity is a functionof the pressure to expand capacity (PEC)

PEC (119905) = DDPCcgdd (8)

The pressure to expand capacity is expressed by the ratio ofthe delivery delay perceived by the company (DDPC) to thecompany goal for delivery delay (cgdd)

DDPC (119905) = smooth (DD 119879cpdd) (9)

The delivery delay perceived by the company is a smoothedvalue of the delivery delay with a timescale of 119879cpdd

The mathematical performance of the system is dictatedby three differential equations In the Simulink representation

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

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DistributedSensor Networks

International Journal of

6 Journal of Industrial Engineering

OR

SR

DP

CAPDCAP

DD

BL

ERR

SF

DOR

SB

SE

DDPMDDPCDD

PEC

EEPDC

sr

dor

Transfer Fcn 4Transfer Fcn 3

Transfer Fcn 2

Transfer Fcn(with initial

Scope 2

SF

OR

Lookup table 2

Lookup table 1

Lookup table

Integrator

Gain 9

Gain 8minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

minusKminus

Gain 6P

Gain 5Gain 4

Gain 2

Gain 1

ER

Divide 5

Divide 4

Divide 3Divide 2

Divide

Constant 20

Constantb0

CAP

BL

Add 4

Add 1

outputs) 1

Transfer Fcn(with initial

outputs)

Transfer Fcn(with initialoutputs) 3

Transfer Fcn(with initialoutputs) 2

++

+

dividetimes

times

times

times

1

sxo

1

1

1

1

dividetimes

minus

TSF

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpd middot s + 1

Figure 3 Simulink version of Stermanrsquos Model

of Figure 3 we use three integrators to solve these equationsthese are shown as integrator blocks The scaling of variablesis achieved with the triangular gain blocks and the output ofvariables shown on oscilloscope blocks Simulink is a generalsimulation package used withMATLAB and is more versatilethan the SD packages in current use Its use allows morecomplex analysis to be used The outputs from the two pack-ages agree well since they solve the same equations generallyusing the same numerical procedures but MATLAB can usedifferent algorithms

The smooth function in (5) and (9) is a higher orderdelay used in SD models rather than a simple exponential

function This usually arises when the information about aprocess takes some time to reach the decision maker and itwill thus take time to register and obtain a response Thecapacity utilisation and the effect of expansion pressure ondesired capacity are implemented in the SD software bysemiempirical lookup tables based on trend observationsof specific real company operations and these produce thehighly nonlinear response For the present model theselookup tables together with the divisors had to be recast ifa linearised control system model was to be created Thedecision tables put into the Sterman model are traditionalSD tabulated functions in this case using ratios of variables

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

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DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 7

Orderfulfillment

Capacityacquisition

Simplebacklogmodel

APVIOBPCSmodel with

limits

Stermanmodel

CS modelFirm

Built-in nonlinearfunction

no separatemanagerial control

SeparatePID control

system

Figure 4 Comparison of the Sterman and new CS Models

such as desired production divided by capacity to give theutilisationThese are implemented as 2D lookup tables in theSimulink model

4 New Model

This section outlines the basis of the new control system (CS)model used to improve the behaviour of a variable capacityfirm The changes from the Sterman model in order for themanager to regain control over the capacity increase processare outlined In the Sterman model the production capacityis outside the control of the order fulfillment organisationIn the new CS model this parameter is brought underthe direct control of management as a key decision factorThe fundamental differences between the two models areindicated in Figure 4 The capacity controller interacts withthe limits in the APVIOBPCS subsystem The inventoryrepresentation in the CS model is comprehensive and thecontrol of the capacity allows automatic variations to reachthe target level of capacity chosen by the manager The newCSmodel is shown in a Simulink implementation in Figure 5

The purpose of the new model variant reported here is toaddress two common issues reported in the literature

(i) Firstly the capacity acquisition process was not timelyenough to prevent companies failing So the aim wasto devise a new decision process that would preventthe oscillatory problems seen in the SD model Thiswas a clear conclusion from the work of ForresterMorecroft and Sterman At a process level it wasalso the conclusion reached by Deif and ElMaraghy[49] The intent therefore was to produce a modelvariant that included some provision of automaticdecisions at least in the operational area to speedup capacity utilisation to provide information that

capacity is effectively being used that can be reliedupon by senior managers

(ii) Secondly the Sterman model does not include theinventory control procedures normally used by man-agers and hence does not include all the associateddelays which would be significant to the operation ofthe whole system Based on this factor alone it wouldbe expected that a real system would respond moreslowly than the Sterman model

The change in the decision process goes to the core of theproblem Sterman [5] has shown experimentally that smallchanges in decisions can have great effects on the responseof the whole process The decision process using differencesrather than ratios is a fundamental change that has significantresults The justification for using straight differences is thatinmost quality procedures using control charts for exampledata is compared directly with set values for tolerances as oneexample So we can argue that managers are already disposedto compare their data with a predisposed set value In mostbiological systems for example a difference is recognisedand acted on The difference between a set value and asystem value is the basis of control for all systems This is adescription of a control system in the regular sense normallycomputed automatically in a control system

These SD lookup tables were then replaced with asmoothed function constant and the formulation of the extracapacity defined by relationships for the error in (ie differ-ence between) capacity (ECAP) and the desired capacity

(i) The delays in the inventory production and forecast-ing process were not modelled in Stermanrsquos workTo include this factor a subsystem model of anautomatic pipeline and variable inventory order basedproduction control system (APVIOBPCS) was addedto the simulation In this implementation the desired

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

8 Journal of Industrial Engineering

SR

BL

DPR

SBDOR

SF SF

DD

SR

R

OR

DOR

diffperr

In 1 Out 2

Capacity subsystem

Transfer Fcn 2

Transfer Fcn(with initial outputs) 1

In 1

In 2

In 3

Out 1

Out 2

Out 3

Subsystem

Step

Saturation 2

SF

Manual switch 1Manual switch

Gain 9

Gain 8

Gain 7

P

Gain 6

Gain 5

ER

Divide 1

Divide DD

0Constant 1

CU

CAP

Add 6

Add 4

++

+minus

divide

dividetimes

times

minusKminus

minusKminus

minusKminus

minusKminus

TransferFcn 1

TransferFcn 5

TransferFcn 4

TransferFcn 3

minus+

TSF

1

Tr middot s + 1

1

Tr middot s + 1

1

Tmdd middot s + 1

1

Tcpdd middot s + 1

1

Tsf middot s + 1

Figure 5 Linear control model with inventory

production could exceed the capacity so a switch wasadded (see subsystem model Figure 6) to prevent theoutput exceeding the current capacity as a simplifiedrealisation of that limit The nonlinear inventorymodel was derived from Spiegler [50]

The error in capacity is defined to be the difference betweenthe demand Orate and the existing capacity

ERRCAP (119905) = OR (119905) minus CAP (119905) (10)

This matches the statement by Sterman given earlier Wepropose thatmanagers recognise differencesmore easily thancomputing ratiosThismay seem as a small difference but hasa larger effect than supposedThe desired capacity DCAP(119905)is now given by the original capacity plus the extra capacityordered ECAP(119905)

DCAP (119905) = CAP (119905) + ECAP (119905) (11)

There is a delay in acquiring capacity caused by both thedelay in recognising that it is needed and also by the time toorder the plant and actually get it into place with attendanttraining delays These delay times are aggregated to a value119879cap We propose using a PID controller to reduce any steadystate error in the capacity required KE is a number relating

the extra capacity proposed to the difference between theorder rate and the existing capacity If the value of KE lt 1then we need less than the difference between order rate andcapacity and if KE gt 1 then we have decided that we needmore capacity than the difference The capacity control loopis described by

119889ECAP (119905)119889119905 = 1119879cap [KE (ERRCAP (119905))

+ KE Iiint (ERRCAP (119905)) 119889119905

+ KEDd(119889ERRCAP (119905)119889119905 ) minus ECAP (119905)]

(12)

One of the fundamental changes in the model structure isseen by comparing (6) and (7) with (10)ndash(12) Figures 5 and6 show the linearised model in Simulink and the subsystemsfor inventory and capacity control The prime differences tothe structure of Figure 3 are seen to be the elimination ofthe lookup tables and the use of the difference between thedesired and actual capacity values as the capacity error signaltogether with the addition of the inventory loop Figure 6shows the addition to the model of a PID control unit actingon the capacity error signal These elements are connected to

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 9

Capacity subsystem

APVIOBPCS loop with capacity limits

CAP

ECAP

DCAP

ERRCAP

1Out 2

Transfer Fcn Saturation

PID

PID controller

Delay transfer Fcn Delay transfer Fcn(with initial outputs) with 1 third time

1 third delay

1 In 1

1

6s + 1

1

6s + 1

1

6s + 1

minus

+

+

+

(with initial outputs) times3

3Out 3

2Out 2

1Out 1

ag8

tpb

1twg5

g4

g3

g2

1tig1

Work in progress

gt

Switch 1 State-space 1

State-space

COMR

Saturation 1

upulo

y

Saturationdynamic

SR

0

Constant 1

invi

Constant

CONS

BL

AINV

3 In 3

2 In 2

1 In 1

+

+

++

+

+

+

+

+

++

+

+

minus

minus

+minus

minus

minus

1

s

1

s

1

s

y = Cx + Dux998400 = Ax + Bu

y = Cx + Dux998400 = Ax + Bu

Add 3

Add 2

1

Tcpd middot s + 1

Figure 6 Capacity and inventory subsystems

a subsystem consisting of an APVIOBPCS inventory modelIn this subsystem actual levels of delivered items are limitedto the current capacity that is controlled by the capacityloop subsystem Only positive production and order rates areallowed by including a saturation block in both paths

The smoothing functions and delays were then replacedby simple first-order delay functions (blocks) In the Simulinkmodels information transmission is represented by the

arrows The overall model is shown in Figures 5 and 6 wherethe smoothing function is replaced by a series of three delaysbetween DCAP and CAP represented by the block transferfunction

Another modification made to Stermanrsquos original SDform was the addition of PID control for the system gains(Figure 6) Apart from this modification the other systemconstants used in this paper are the same as used by Sterman

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

10 Journal of Industrial Engineering

0 20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Time (months)

StermanKE = 3

KE = 15KE = 1

Sale

s

Figure 7 Order rate performance of the two models

PID control has been widely used in industry and has a termthat allows for rates of change to be smoothed and long termerrors to be eliminated It includes a term as in the Stermanmodel proportional to the input and including a term thatintegrates the error and a term proportional to the rate ofchange of the error

The justification for including PID functions followsfrom Diehlrsquos [51] work that suggests that when managersare expected to make decisions about process orders theyare unable to make predictions that include a measure oftrends and allowance formaterial in the pipelineThis is oftenbecause of the long time-scales in inventory processes Thestrategic scaling issues considered here could be of an evenlonger timescale and we believe that managers cannot detectlong term trends allowing for the effects of variation of rate ofchange This will be taken care of by the PID controller

The CS model can be compared to the very muchsimpler models of White and Censlive [52 53] The resultsof a comparison of the responses of two implementationsSterman and CS are shown in Figures 7ndash23 KE here isthe control factor in the hands of the manager where theycan decide to increase the amount of capacity deficit toimplement

5 Results

In this section the results from the two models Stermanrsquosmodel and the new CS model will be compared Two sets ofresults are presented here the first set of results is for the casewhere there is no exogenous or external input here sales aregenerated by the in-house sales force

Figure 8 illustrates the response of both the Simulinkversion of Stermanrsquos model and the new control system (CS)model In this figure the solid line is the Sterman SD modeldata from the Simulink version using Euler integrationHowever the Sterman model results differ significantly fromthose of the linearised control model shown with the dashedline for KE = 3 and by the dotted line for KE = 15 whichdoes not show the large oscillations Significantly the curvefor KE = 1 shows that the sales decline to zero after 100months This is because the projected capacity cannot matchdemand The behaviour predicted by the Sterman model is

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 8 Shipment rate

StermanNLInvent KE = 15NLInvent KE = 3

20 40 60 80 100 120 1400Time (months)

0

2

4

6

8

10

12

Deli

very

del

ay

Figure 9 Delivery delay

that the company goes through repeated boom and bustcycles During the sales slumps the orders drop by up to 50Thiswould probably cause themanagers to be fired and severeretrenchment in the business The business might even besubject to takeover during this phase The slump in sales forthe CS model is catastrophic for the company It could beavoided by timely increase in capacity

It is clear that the structure of the SD model and hencethe company upon which it is based has serious structuralflaws if operated as the model predicts Since the decisionprocesses are fairly simple we can see what the effect of thenonlinear functions is since these introduce higher orderdynamics From experiments conducted by Sterman it is clearthat managers cannot readily appreciate these higher orderdynamics The key to controlling the growth of this companywould be to increase capacity in a timely manner Using theCS model it is easier to see when to implement capacitychanges

The control system model for different values of propor-tional gain KE provides a similar range of results to thoseof the Sterman model but without the large oscillationsThe sales rate (Figure 7) is in line with the values shownfor the Sterman model But for the shipment rate (Figure 8)

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 11

1

StermanNLInvent KE = 3NLInvent KE = 15

02

04

06

08

12

14

16

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 10 Capacity utilisation

StermanNLInvent KE = 15NLInvent KE = 3

0

200

400

600

800

1000

1200

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 11 Sales force

they are higher than those of Sterman for KE gt 2 The newmodel (Figure 9) shows that the delivery delay rises to 8months for the low gain KE = 15 whereas the Stermanmodeloscillates around 2ndash8 months while the CS model with KE= 3 is no worse than the Sterman model at just below 8months Capacity utilisation in the Sterman model is at 130for considerable periods of time whereas the CS model runsat around 100 except at the start of the process implyingconsiderable overtime working of plant and staff The valueof utilisation means we would have to run with significantovertime with consequences for profitability The peak valueof sales force (Figure 11) is higher for KE = 3 but for alarger sales it is the same It is not clear why with a highershipment rate the backlog (Figure 11) is also higher for the CSmodel However matching the higher shipments and ordersthe required capacity is also higher in Figure 13

Figure 14 shows that the revenue is higher for the wholeperiod for KE = 3 but generally for KE = 15 in a similaramount The large swings seen in the Sterman model are notseen in the CS PID controlled system The key problem formanagers is that the large swings in performance are seen asbeing due to external factors but are in fact due entirely to thestructure of the system for implementing decisions

Sterman

NLInvent KE = 3NLInvent KE = 15

0

05

1

15

2

25

3

35

Back

log

20 40 60 80 100 120 1400Time (months)

times104

Figure 12 Backlog

StermanNLInvent KE = 3NLInvent KE = 15

0

1000

2000

3000

4000

5000

Capa

city

0 40 60 80 100 120 14020Time (months)

Figure 13 Capacity

The variation in capacity will be a severe problem to dealwith as an investment issue The system responses show alower average and peak backlogThese excessive backlog anddelivery delays will cause loss of customers and may resultin them moving to a rival supplier Shipment rates also varygreatly in the Sterman model creating logistic problems notpresent in the control system data

The final curve shown in Figure 15 is the net stock in theinventory not computed in the Sterman model This shows asubstantial excess stock problem after 60 months A variablegain could be used by managers to control this parameter

A step exogenous demand is made for the second setof results This represents a sudden surge in customers sayfrom an advertising campaign The picture (Figures 16ndash23)is not quite so clear nowThe CS model (Figure 16) predicts aslower rise in shipment rate due to the delays in the inventoryand forecasting elements For KE = 3 the shipment rateexceeds 650 unitsmonth but then drops back to 600 after65 months The reduction in capacity predicted (Figure 17)by the Sterman model is not the same in the CS model thiswould appear to be due to the dynamics in the original modelnot replicated in the CS model Even for the CS model with

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Industrial Engineering

StermanNLInvent KE = 15

NLInvent KE = 3NLInvent KE = 1

0

1

2

3

4

5

Expe

cted

reve

nue

20 40 60 80 100 120 1400Time (months)

times107

Figure 14 Expected revenue

KE = 3KE = 15

20 40 60 80 100 120 1400Time (months)

0

200

400

600

800

1000

AIN

V

Figure 15 Net stock

KE = 15 the capacity is increased more quickly than for theStermanmodel whereas the sales force required (Figure 18) isvery close in the two models The controlled system deliverydelay can be made to reach zero for KE = 3 (Figure 19)The CS model has a higher peak backlog (Figure 20) butthis reaches zero and the capacity utilisation required bythe control system models is now not excessive being closeto 100 but dropping to 92 since excess capacity is nowin place Apart from a small period around 10 months theinventory is close to zero unless the sales have crashed (KE= 1) The expected revenue is slightly greater for the case ofKE = 3

These results show that the CS model allows better use ofthe existing capacity and allows extra capacity to be scheduledfaster than the SD model

6 Discussion

The implications of the results of the simulations are now dis-cussed with the possible implications for managers outlined

The control system models agree with the general trendsof the variables from the Sterman SD model but they do notexhibit large oscillations present in the SD model Responsesare adjusted by altering the error gain The main differencebetween the Sterman SD model and our model is the way

Sterman modelInventory model KE = 3Inventory model KE = 15

500520540560580600620640660

Ship

ping

rate

20 40 60 80 100 120 1400Time (months)

Figure 16 Exogenous step input shipment rate

StermanNLInvent KE = 3NLInvent KE = 15

450

500

550

600

650

700

Capa

city

20 40 60 80 100 120 1400Time (months)

Figure 17 Exogenous input step capacity response

the errors are computed and the nonlinear gains set inthe Sterman model lookup tables The loop structure anddelays are the same except for the addition of the inventorysubsystem loops in the CS model It is clear therefore thatthe violent oscillations in capacity response which causemajor business operational problems are due to the waythe decisions are implemented If a model can be used thatdoes not exhibit these decision trends then a growth periodfor the company is more likely These results also broadlyagree with those of Yuan and Ashayeri [29] The capacityaugmentation behaviour under external input is similar tothat described by Kamath and Roy [30] Since no nonlinearlimits are included in the CS model its capacity utilisation isshown to be considerably higher in the Sterman SD modelfor the input conditions whereas peak utilisations are lowerfor the PID controlled system model

Sterman [4] points out that his growth model showsfar from optimal company performance Growth is smallerthan it could be Actual company growth is smaller than itcould be and also growth of the firm is not smooth beingsubject to repeated ldquoboom and bustrdquo cycles The analysispresented here suggests that these cycles are entirely due tothe structure of the decision-making process incorporatedinto the firmsrsquo management organisation Sterman discussesat length the implication for thewaymanagers operate in suchan environment Seniormanagers have the tendency to blamemiddle managers for weak leadership instead of examiningthe decision structures implemented in the firm One cause

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 13

StermanNLInvent KE = 15NLInvent KE = 3

020406080

100120140160

Sale

s for

ce

20 40 60 80 100 120 1400Time (months)

Figure 18 Step input sales force

StermanKE = 15KE = 3

minus1

0

1

2

3

4

5

Deli

very

del

ay

20 40 60 80 100 120 1400Time (months)

Figure 19 Step input delivery delay

is the inability of people to recognise the cause and effectwhen the events are not close together in time (and in anotherdepartment) If we change that process reducing the timebetween event and action and making it easier to recognisean event by highlighting differences in performance as in theCS model presented here the causes of boom and bust cyclescould be eliminated from internal mechanisms within thecompanyThose causes remainingwill then be due to externalevent cycles in the economy as a whole

7 Conclusions

Conclusions can be drawn from the responses of the twomodels and the work of other researchers

Examination of the literature about capacity provisionshows that the problem of capacity planning in high-tech andlow-tech firms is a serious problem exacerbated in high-techproducts by the short lifetime Existing industry data showscyclic variation of capacity and investment to be present SDanalysis has shown this to be largely a company managementstructural effect rather than a demand problem

Sterman created an SD model to examine the criticalaspects of management decision-making after his investi-gation of feedback decisions in supply chains His modelshows unacceptably large cyclic variations in capacity Toreduce these effects a different decision process was devised

StermanNLInvent KE = 15NLInvent KE = 3

minus5000

50010001500200025003000

Back

log

20 40 60 80 100 120 1400Time (months)

Figure 20 Step input effect on backlog response

StermanKE = 3KE = 15

09095

1105

11115

12125

Capa

city

util

isatio

n

20 40 60 80 100 120 1400Time (months)

Figure 21 Step input on capacity utilisation

and a control engineering based (CS) model of the strategicmodification of available capacity has been devised to includenormal inventory control and delays to compare with thestandard SD model of strategic capacity acquisition by Ster-man

This new model shows very clearly the effect the decisionstructure has on company performance by comparison withthe model of existing companies from Sterman It shouldbe appreciated that nearly all SD models have embeddedindustry or company data in the nonlinear table functionsused as they are often created for consultancy and are thenspecific to particular companies

We have shown that an alteration to the decision processto make the recognition of the changes in capacity byimplementing a simple difference between what is neededand what is already in place has a profound impact on theresponse to external demand

The CS model does not use the nonlinear functionsfor decisions that the SD model uses making it easier formanagers to understand and recognise the process WhenPID control is used the performance is improved for manyinput conditions but a simple system using just the gainKE will have many of the overall advantages The extremebooms and crashes predicted by the Sterman SD model arenot present in this scenario from the model presented hereHence internal decision processes can be eliminated being

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Journal of Industrial Engineering

KE = 1KE = 3KE = 15

0 20 60 80 100 120 14040Time (months)

minus500

0

500

1000

1500

2000

2500

AIN

V (u

nits)

Figure 22 Net stock responses for step input in demand

StermanNLInvent KE = 3NLInvent KE = 15

20 40 60 80 100 120 1400Time (months)

01234567

Expe

cted

reve

nue

times106

Figure 23 Order rate gain variation

the cause of their company suffering ldquoboom and bustrdquo cyclesHowever the gain of the capacity controller altered by themanager must be greater than 1 to avoid a company crash dueto insufficient capacity

Shipment rates occur later in the CSmodel for exogenousdemand due to the inventory delays and themodel shows thatcapacity utilisation is closer to 100 than that reported for theSD model This is also true when a sudden external demandis made Peak delivery delay and staff levels are similar to thePID controlled system model

The control system model has

(i) reduced variation in sales rates capacity deliverydelay and backlog

(ii) more consistent shipment rates

(iii) more consistent revenue rates

TheCSmodel is more generally applicable since it has limiteddata embedded in it that cannot be altered to suit a differentcompany

Themodel is able to providemanagement guidance at thestrategic level and ease the decision-making process enablinga choice of system parameters to give a specific performance

The internal feedback mechanisms in the model allow man-agers to examine and rectify the effects on the companyoperations due to poor management decisions

This model can easily be implemented as a spreadsheetfor use by managers using only simple sales and other data

The significant lesson from this work is that small changesin decisions can have large effects on the behaviour of thewhole productionsupply system These changes togetherwith making the decision at the correct time will determinethe success of the strategy

These models presented here are probably too simple tofully represent a particular company without adding extradetails but those parameters taken as constants need tobe examined to determine their contribution to successfulbusiness operation For example the company goal fordelivery delay could be made a dynamic variable

Future Work

The control system model allows the examination of theeffects of adverse events such as production line machinefailures or external commercial environmental factors bysimulation of random capacity disturbances Future researchwill examine the effect of policy analysis on sales forceproductivity the increasing use of internet marketing plusorder systems the freeing up of the concept of fixed deliv-ery delays and more rapid reconfiguration of productionfacilities Since it is difficult to gain the trust of companymanagers to implement such processes without evidence oftheir effectiveness this model could be developed into aproduct similar to the ldquoBeerGamerdquo as amanagement trainingaid to demonstrate the effectiveness of control of internaldecision interactions

Abbreviations

BL Backlog (units)b0 Initial backlog = 1000CAP Capacity (units)Cgdd Company goal for delivery delay = 2

monthsCor Gain of sales forceCSR Cost per sales rep = $8000CU Capacity utilisation (fraction of capacity in

use)DCAP Desired capacity (units)DD Delivery delay (weeks)Dd Derivative gain for PID sim 05DDPC Delivery delay perceived by the company

(weeks)DP Desired production (units)ECAP Extra capacity (units)EEPDC Effect of expansion pressure on desired

capacityER Expected revenueERRCAP Error in capacityFRS Fraction of revenue to sales = 02Ii Integral gain sim 0001KE Control system proportional gain sim 25

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Industrial Engineering 15

Kor Gain of backlog feedbackMPS Management planning systemMTDD Market target delivery delay = 2 monthsNDD Normal delivery delay (company target)

(weeks)NSE Normal sales effectiveness = 10OR Order rate (unitstime)ori Initial value of order rate119875 Price of product = $10000PCB Printed circuit boardPEC Pressure to expand capacityPID Proportional Integral and DerivativePPC Production Planning and Control systemSALES Sales rate119904 Laplace transformSB Sales budgetSFAT Sales force adjustment timeSR Shipment rate (unitstime)119879cpd Time to perceive capacity deficit = 3 months119879cap Time for capacity acquisition delay = 18

months119879cpdd Time for company to perceive delivery delay

= 3 months119879mdd Time for market to perceive delivery delay =

12 months119879r Revenue reporting delay = 3 months119879sf Sales force adjustment time = 18 months

Competing Interests

The authors declare that they have no competing interests

References

[1] J D Sterman and EMosekilde Business Cycles and LongWavesA Behavioural Disequilibrium Perspective WP3528-93-MSAMIT Press Cambridge Mass USA 1993

[2] R G King and S T Rebelo ldquoResuscitating real business cyclesrdquoinHandbook of Macroeconomics J B Taylor andMWoodfordEds North Holland Amsterdam The Netherlands 1999

[3] European Commission European Business Cycle Indicatorsmdash2nd Quarter 2013 2013

[4] J D Sterman Business Dynamics McGraw-Hill Boston MassUSA 2000

[5] J D Sterman ldquoModeling managerial behavior misperceptionsof feedback in a dynamic decision making experimentrdquo Man-agement Science vol 35 no 3 pp 321ndash339 1989

[6] J Lyneis ldquoSystem dynamics in business forecasting A CaseStudy of the Commercial Jet Aircraft Industryrdquo in Proceedingsof the 16th System Dynamics Conference Quebec Canada July1998

[7] P Langley M Paich and J D Sterman ldquoExplaining capac-ity overshoot and price war misperceptions of feedback incompetitive growth marketsrdquo in Proceedings of the 16th SystemDynamics Conference Quebec Canada July 1998

[8] J Forrester ldquoMarket growth as influenced by capital invest-mentrdquo Industrial Management Review vol 9 no 2 pp 83ndash1051968

[9] O Nord Growth of a New Product Effects of Capacity Acquisi-tion Policies MIT Press Cambridge Mass USA 1963

[10] J DMorecroft ldquoSystem dynamics portraying bounded realityrdquoin Proceedings of the System Dynamics Research Conference TheInstitute on Man and Science Rensselaerville NY USA 1981

[11] J D Morecroft ldquoSystem dynamics portraying bounded ratio-nalityrdquo Omega vol 11 no 2 pp 131ndash142 1983

[12] J D Morecroft ldquoStrategy support modelsrdquo Strategic Manage-ment Journal vol 5 no 3 pp 215ndash229 1984

[13] N A Bakke and R Hellberg ldquoThe challenges of capacityplanningrdquo International Journal of Production Economics vol30-31 pp 243ndash264 1993

[14] F M Bass ldquoA new product growth for model consumerdurablesrdquoManagement Science vol 15 no 5 pp 215ndash227 1969

[15] F M Bass T V Krishnan and D C Jain ldquoWhy the bass modelfits without decision variablesrdquoMarketing Science vol 13 no 3pp 203ndash223 1994

[16] R Wild Production and Operations Management CassellLondon UK 5th edition 1995

[17] H A Akkermans P Bogerd E Yucesan and L N Van Was-senhove ldquoThe impact of ERP on supply chain managementexploratory findings from a European Delphi studyrdquo EuropeanJournal of Operational Research vol 146 no 2 pp 284ndash3012003

[18] S Karrabuk and D Wu ldquoCoordinating Strategic CapacityPlanning in the semi-conductor industryrdquo Tech Rep 99T-11Department of IMSE Lehigh University Bethlehem Pa USA1999

[19] S D Wu M Erkoc and S Karabuk ldquoManaging capacity inthe high-tech industry a review of literaturerdquo The EngineeringEconomist vol 50 no 2 pp 125ndash158 2005

[20] A Adl and J Parvizian ldquoDrought and production capacity ofmeat A system dynamics approachrdquo in Proceedings of the 27thSystemDynamics Conference vol 1 pp 1ndash13 Albuquerque NMUSA July 2009

[21] O Ceryan and Y Koren ldquoManufacturing capacity planningstrategiesrdquo CIRP AnnalsmdashManufacturing Technology vol 58no 1 pp 403ndash406 2009

[22] A S White and M Censlive ldquoAn alternative state-spacerepresentation for APVIOBPCS inventory systemsrdquo Journal ofManufacturing Technology Management vol 24 no 4 pp 588ndash614 2013

[23] J W Forrester Industrial Dynamics MIT Press Boston MassUSA 1961

[24] B J Angerhofer and M C Angelides ldquoSystem dynamicsmodelling in supply chain management research reviewrdquo inProceedings of the 2000 Winter Simulation Conference pp 342ndash351 New Jersey NJ USA December 2000

[25] E Suryani ldquoDynamic simulation model of demand forecastingand capacity planningrdquo in Proceedings of the Annual Meeting ofScience and Technology Studies (AMSTECS rsquo11) Tokyo JapanMarch 2011

[26] S Rajagopalan and J M Swaminathan ldquoA coordinated pro-duction planningmodel with capacity expansion and inventorymanagementrdquo Management Science vol 47 no 11 pp 1562ndash1580 2001

[27] E G Anderson Jr D JMorrice andG Lundeen ldquoThe lsquophysicsrsquoof capacity and backlog management in service and custommanufacturing supply chainsrdquo SystemDynamics Review vol 21no 3 pp 217ndash247 2005

[28] J D Sterman R Henderson E D Beinhocker and L I New-man ldquoGetting big too fast strategic dynamics with increasingreturns and bounded rationalityrdquoManagement Science vol 53no 4 pp 683ndash696 2007

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

16 Journal of Industrial Engineering

[29] X Yuan and J Ashayeri ldquoCapacity expansion decision in supplychains a control theory applicationrdquo International Journal ofComputer Integrated Manufacturing vol 22 no 4 pp 356ndash3732009

[30] N B Kamath and R Roy ldquoCapacity augmentation of a supplychain for a short lifecycle product a system dynamics frame-workrdquo European Journal of Operational Research vol 179 no 2pp 334ndash351 2007

[31] D Vlachos P Georgiadis and E Iakovou ldquoA system dynamicsmodel for dynamic capacity planning of remanufacturing inclosed-loop supply chainsrdquo Computers amp Operations Researchvol 34 no 2 pp 367ndash394 2007

[32] N Duffie A Chehade and A Athavale ldquoControl theoreticalmodeling of transient behavior of production planning andcontrol a reviewrdquo Procedia CIRP vol 17 pp 20ndash25 2014

[33] H-P Wiendahl and J-W Breithaupt ldquoAutomatic productioncontrol applying control theoryrdquo International Journal of Pro-duction Economics vol 63 no 1 pp 33ndash46 2000

[34] P Nyhuis ldquoLogistic production operating curvesmdashbasic modelof the theory of logistic operating curvesrdquo CIRP AnnalsmdashManufacturing Technology vol 55 no 1 pp 441ndash444 2006

[35] F M Asi and A G Ulsoy ldquoCapacity management in reconfig-urable manufacturing systems with stochastic market demandrdquoin Proceedings of the ASME International Mechanical Engineer-ing Congress (IMEC rsquo02) pp 1562ndash1580 New Orleans La USANovember 2002

[36] S-Y Son T L Olsen and D Yip-Hoi ldquoAn approach toscalability and line balancing for reconfigurable manufacturingsystemsrdquo Integrated Manufacturing Systems vol 12 no 6-7 pp500ndash511 2001

[37] J A Sharp and R M Henry ldquoDesigning policies the zieglernichols wayrdquo Dynamica vol 5 no 2 pp 79ndash94 1979

[38] D R Towill and S Yoon ldquoSome features common to inventorycosts and process controller designrdquo Engineering Costs andProduction Economics vol 6 pp 225ndash236 1981

[39] A S White ldquoSystem Dynamics inventory management andcontrol theoryrdquo in Proceedings of the 12th International Confer-ence onCADCAMRobotics and Factories of the Future pp 691ndash696 1996

[40] S R Orcun R Uzsoy and K Kempf ldquoUsing system dynamicssimulations to compare capacity models for production plan-ningrdquo in Proceedings of theWinter Simulation Conference (WSCrsquo06) pp 1855ndash1862 IEEE Monterey Calif USA December2006

[41] S Elmasry M Shalaby and M Saleh ldquoA system dynamicssimulationmodel for scalable-capacitymanufacturing systemsrdquoin Proceedings of the 30th International Systems DynamicsConference St Galen Switzerland 2012 httpswwwsystem-dynamicsorgconferences2012proceedindexhtml

[42] P Georgiadis D Vlachos and G Tagaras ldquoThe impact ofproduct lifecycle on capacity planning of closed-loop supplychains with remanufacturingrdquo Production andOperationsMan-agement vol 15 no 4 pp 514ndash527 2006

[43] P Georgiadis and A Politou ldquoDynamic Drum-Buffer-Ropeapproach for production planning and control in capacitatedflow-shop manufacturing systemsrdquo Computers and IndustrialEngineering vol 65 no 4 pp 689ndash703 2013

[44] P Georgiadis ldquoAn integrated system dynamics model forstrategic capacity planning in closed-loop recycling networks adynamic analysis for the paper industryrdquo Simulation ModellingPractice andTheory vol 32 pp 116ndash137 2013

[45] P Georgiadis and E Athanasiou ldquoFlexible long-term capacityplanning in closed-loop supply chains with remanufacturingrdquoEuropean Journal of Operational Research vol 225 no 1 pp 44ndash58 2013

[46] S Cannella E Ciancimino and A C Marquez ldquoCapacityconstrained supply chains a simulation studyrdquo InternationalJournal of Simulation and Process Modelling vol 4 no 2 pp139ndash147 2008

[47] D PackerResource Acquisition in Corporate GrowthMITPressCambridge Mass USA 1964

[48] M Leihr A Groszligler and M Klein ldquoUnderstanding businesscycles in the airline marketrdquo in Proceedings of the 7th SystemDynamics Conference Wellington New Zealand July 1999

[49] A M Deif and H A ElMaraghy ldquoA multiple performanceanalysis of market-capacity integration policiesrdquo InternationalJournal ofManufacturingResearch vol 6 no 3 pp 191ndash214 2011

[50] V L N Spiegler Designing supply chains resilient to nonlinearsystem dynamics [PhD thesis] Cardiff University CardiffWales 2013

[51] E W Diehl Effects of feedback structure on dynamic decisionmaking [PhD thesis] Sloan School of Management MIT NewYork NY USA 1992

[52] A S White and M Censlive ldquoA new control model forstrategic capacity Acquisitionrdquo in Proceedings of the Advancesin Manufacturing Technology XXV 9th International ConferenceonManufacturing Research D K Harrison BMWood andDEvans Eds vol 97 pp 157ndash163 Glasgow UK 2011

[53] A S White and M Censlive ldquoObservations on control modelsfor reconfigurable manufacturerdquo in Advances in ManufacturingTechnologyXXVNinth International Conference onManufactur-ing Research D K Harrison B M Wood and D Evans Edspp 163ndash170GlasgowCaledonianUniversityGlasgowUK 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of