the effect of shop floor continuous improvement programs

7/31/2019 The Effect of Shop Floor Continuous Improvement Programs

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ORIGINAL ARTICLE

The effect of shop floor continuous improvement programs

on the lot sizecycle time relationship in a multi-product

single-machine environment

Moacir Godinho Filho & Reha Uzsoy

Received: 27 August 2008 /Accepted: 2 June 2010# Springer-Verlag London Limited 2010

Abstract While continuous improvement on the shop floor is

a major component of many popular management movementssuch as lean manufacturing and Six Sigma, there are few

quantitative studies of the cumulative effects of such

improvement programs over time. On the other hand, lot

sizing has long been recognized as an important problem in

manufacturing management. In this paper, we use a system

dynamics model based on the Factory Physics relationships

proposed by Hopp and Spearman [1] to examine the effect of

different continuous improvement programs on the relation-

ship between lot sizes and cycle times. We compare two

different types of improvement programs: large improve-

ments in a single parameter, such as might be obtained by a

focused project, or small improvements in many parameters

simultaneously. Our results show that the relationship

between lot sizes, cycle times, and shop floor parameters is

complex and nonlinear. The cycle time benefits of improve-

ments in shop floor parameters are significantly enhanced by

the reduced lot sizes they enable; on the other hand, a poor

choice of lot sizes can negate the benefits of a continuous

improvement program. Although the largest cycle time

reduction is achieved by a large reduction in setup time,

small, simultaneous improvements in several parameters can

achieve much of the same benefit. The cycle time benefits of

multiple simultaneous improvements are mutually reinforc-ing, creating a positive feedback between shop floor

improvements and reduced lot sizes. Our model yields

insight into why the Toyota Production System has been

able to obtain such excellent results over time, and suggests a

number of interesting future directions.

Keywords Lot size . Cycle time .

Continuous improvement. System dynamics .

Factory physics .

Multi-product single-machine environment

1 Introduction

According to Buffa [2], manufacturing decisions, such as lot

sizing, can have major strategic implications for the firm. An

extensive literature on lot sizing problems exists [3, 4], most

of which seeks to find an optimal lot size (called Economic

Order Quantity (EOQ) or Economic Production Quantity)

that achieves the optimal tradeoff between fixed costs of

ordering and inventory holding costs. Reviews of the lot

sizing literature are available in [3, 4]. Despite its benefits,

the EOQ model has been criticized in the literature, for

failing to consider several key issues such as uncertainty in

demand and resources with limited capacity [5].

According to Kuik and Tielemans [6], criticism of cost

accounting methods for production planning led to a

growing interest in physical measures of manufacturing

performance. One such measure is manufacturing cycle

time (also known as lead time or flow time), defined as the

mean time required for a part to complete all its processing.

Time-based competition [7], initially proposed by Stalk [8],

focuses on cycle time reduction as a primary manufacturing

M. Godinho Filho (*

)Departamento de Engenharia de Produo,

Universidade Federal de So Carlos,

Via Washington Luiz, km 235, Caixa Postal 676, So Carlos,

SP 13.565-905, Brazil

e-mail: [email protected]

R. Uzsoy

Edward P. Fitts Department of Industrial and Systems

Engineering, North Carolina State University,

Campus Box 7906,

Raleigh, NC 27695-7906, USA

e-mail: [email protected]

Int J Adv Manuf Technol

DOI 10.1007/s00170-010-2770-8


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goal. Despite this interest in cycle time reduction, de

Treville et al. [9] point out that the literature on cycle time

reduction has been largely anecdotal and exploratory.

Some exceptions are the Factory Physics work of Hopp and

Spearman [1, 10], and the Quick Response Manufacturing

approach of Suri [11] that use queuing theory to develop a

set of relationships between throughput, cycle time and

critical shop floor parameters, aiming to increase themanagers understanding of manufacturing dynamics. One

such is the relationship between lot size and average cycle

time, which is studied in this paper. Karmarkar et al. [12]

first introduced the convex relationship between lot size

and average cycle time. This relationship is derived from

queuing theory, specifically the Kingman approximation of

the expected cycle time in system for the G/G/1 queue [1],

and is illustrated in Fig. 1. Lambrecht and Vandaele [13]

describe this relationship: Large lot sizes will cause long

cycle times (the batching effect); as the lot size gets smaller

the cycle time will decrease but once a minimal lot size is

reached a further reduction of the lot size will cause hightraffic intensities resulting in longer cycle times (the

saturation effect).

Several other papers have used queuing models and

simulation to study the relationship between lot size

decisions and cycle time. Karmarkar et al. [14] present

heuristics for minimizing average queue time. Rao [15]

discusses alternative queuing models in relation to lot sizes

and cycle time. Lambrecht and Vandaele [12] develop

approximations for the expectation and variance of the

cycle time under the assumption of individual arrival and

departure processes. Kenyon et al. [16] use simulation to

evaluate the impact of lot sizing decisions on cycle time in

a semiconductor company. Vaughan [17] uses queuing

relationships to model the effects of lot size on cycle time.

Other papers relating lot size and cycle times are [1820].

Although these studies provide a basis for understanding

the relationship between lot sizes and cycle times, there is

no literature showing the impact of continuous improve-

ment (CI) efforts on this relationship. This is despite the

repeated observation that reduction of lot sizes and cycle

times is a critical component of lean manufacturing and the

Toyota Production System [21]. In this context, this paper

compares the effect of six shop floor continuous improve-

ment programs on the lot size-cycle time relationship in a

multi-product, single-machine environment using a combi-

nation of system dynamics and factory physics approaches.

The next section gives a short review of the relevant

literature on CI and the two modeling approaches used inthis paper (system dynamics and factory physics); Section 3

presents the model developed and the experimental design

and Section 4 the results of the experiments. We conclude

the paper in Section 5 with a summary and some future

directions.

2 Literature review

2.1 Continuous improvement

Caffyn [22] defines continuous improvement as a massinvolvement in making relatively small changes which are

directed towards organizational goals on an ongoing basis.

Continuous improvement has been recognized for many years

as a major source of competitive advantage, and is inherent in

many recent management movements such as the Theory of

Constraints [23], Six Sigma [24] and the Toyota Production

System [21]. Inability to effectively implement continuous

improvement programs is seen by many scholars and

practitioners as one of the reasons why Western firms have

not fully benefited from Japanese management concepts

[25]. Savolainen [26] points out that CI is a complex process

that cannot be achieved overnight, but involves considerable

learning and fine tuning of the mechanisms used. The core

principles of CI are, according to Imai [27]:

1. process orientation

2. small step improvement of work standards

3. people orientation.

Leede and Looise [28] suggest that the main issue

regarding CI is the problem of combining extensive

employee involvement with market orientation and present

the mini-company concept, which they claim incorporates

these elements. However, there appears to be a lack of

quantitative studies examining how different CI approaches

affect manufacturing performance over time.

In this paper, we deal with CI in six different shop floor

parameters: (1) arrival variability, (2) process variability

(natural process time variability, repair time variability and

set up time variability), (3) quality (mean defect rate), (4)

mean time to failure, (5) mean repair time, and (6) mean set-up

time. Basically, these improvements deal with improvement in

different parameters: mean times and rates and their variabil-

ity, measured in terms of coefficient of variation (cv).

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600 700

Lot size (pieces)

CycleTime(hours)

Fig. 1 Relationship between lot size and cycle time



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Hopp and Spearman [1] indicate that increasing variability

always degrades the performance of a production system in

terms of cycle time, work in process inventory (WIP) level or

throughput. So, if a company cannot reduce variability, it will

pay in one or more of the following ways: reduced throughput,

increased cycle times, higher inventory levels and long lead

times [1]. Schoemig [29] presents a simulation study illustrat-

ing the corrupting influence of variability caused by machineand tool unavailability on manufacturing performance.

Although the negative effects of variability are well

known, there is little research examining the dynamic

behavior of these effects over time, especially when linked

to other shop-floor parameters. Newman et al. [30] claim

that reducing variability and increasing flexibility enable

capacity, inventory and time to be reduced, increasing

companys performance; Mapes et al. [31], by means of a

study in 963 manufacturing plants in UK, determine that

the high performance companies utilize processes and

procedures that have low levels of variability and uncer-

tainty. Despite this conclusion, these authors state that theirpaper considers the performance of the plants at a particular

point of time, and suggest studies of the relation between

variability reduction and performance in a dynamic envi-

ronment in the face of ongoing reductions in variability,

which is exactly the issue addressed in this paper.

The literature suggests a number of methods that can help

reduce the arrival and the process variability. For reducing

arrival variability, Hopp and Spearman [1] suggest: (1)

decreasing process variability at upstream stations, (2) better

scheduling and shop floor control to smooth material flow, (3)

eliminating batch releases, and (4) installing a pull production

control system such as Constant Work in Process or Kanban

[21]. For a review about kanban variations see Lage Jr and

Godinho Filho [32]. They formalize the relationship between

different shop floor parameters in the form of a diagnostic tree

[33]. Process variability is routinely addressed in practice

using techniques such as Six Sigma, operator training,

standardized work practices and automation. Other methods

to improve manufacturing parameters include the Single

Minute Exchange of Die system [34] to reduce the mean set

up time; Total Productive Maintenance [35] to achieve

improvements in mean repair time and mean time to failure;

and finally, quality control methods like Statistical Process

Control, Six Sigma and Total Quality Management to reduce

mean defect rate, Lean Manufacturing [36], Quick Response

Manufacturing [11], among others.

Table 1 shows examples of methodologies/tools used to

improve the shop floor parameters studied in this paper.

2.2 System dynamics

System dynamics (SD) were developed by Jay Forrester in

1956 at the Massachussets Institute of Technology [37]. In

complex systems such as manufacturing systems objects

interact and a change in one variable affects other variables

dynamically, which feeds back the original variable, and so

on [38]. An excellent introduction to system dynamics

modeling is given by Sterman [39].

The structure and the relationship between variables in

an SD model are represented by means of causal loop

diagrams or stock and flow diagrams [39]. In this paper, we

use the causal loop diagram, which has four main elements:

(a) Stocks that characterize the state of the system and

generate the information upon which decisions and

actions are based [39]. The stock level is given by thedifference between cumulative inflow and outflow.

(b) Flows that lead to the increase or decrease of stocks.

These represent the dynamic behavior of the system

over time and may depend on the stock levels.

(c) Auxiliary variables that may be functions of stocks, as

well as constants or exogenous inputs [39].

(d) Links that represent information exchange between

stocks, flows and auxiliary variables.

System dynamics models have been used to address

problems in a wide variety of areas [40, 41]. However,

there is a lack of SD applications to manufacturing systems,

despite evidence that this technique is suitable for industrial

modeling. Baines and Harrison [42] point out that the

computer simulation of manufacturing systems is common-

ly carried out using Discrete Event Simulation, and suggest

that manufacturing system modeling represents a missed

opportunity for SD. This is also the opinion of Lin et al.

[43], who propose a framework to help industrial managers

apply SD to manufacturing system modeling. This is one of

our motivations for the work in this paper. Recent advances

in interactive modeling, tools for representation of feedback

Table 1 Examples of methodologies/tools used for shop floor

improvement

Shop floor variable Examples of methodologies/tools

used to improve such variables

(1) arrival variability (cv) decreasing process variability at

upstream stations; using a better

scheduling and shop floor control

to smooth material flow; eliminatingbatch releases, and; installing a pull

production control system

(2) process variability (cv) Six sigma, operators training,

standardizing work practices

and automation

(3) mean defect rate SPC, Six Sigma and TQM

(4) mean time to failure TPM

(5) mean repair time TPM

(6) mean set up time SMED

TQM Total Quality Management



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structure, and simulation software make SD models much

more accessible to practitioners than they have been in the

past [39].

2.3 Factory physics

The Factory physics approach was created by Hopp and

Spearman [1, 10]. This approach is based on a set ofmathematical principles derived from queuing theory. It

has, according to Hopp and Spearman [10], three proper-

ties: it is quantitative, simple and intuitive; so it provides

managers with valuable insights. The basic approach

consists of a set of equations that relate the long-run steady

state means and variances of critical performance measures

such as cycle time and WIP levels to the mean and variance

of system parameters such as time between failures, setup

times and processing times.

As noted by Standridge [44], factory physics provides a

systematic description of the underlying behavior of a

production system. This description can provide supportssimulation studies in the following ways:

1. It helps in deciding what performance measures to

collect and what alternatives to evaluate as well as in

interpreting simulation results.

2. It helps identify the properties of systems that may be

important to include in models.

3. It provides an analytic foundation that helps in under-

standing the behavior of systems and gives insight into the

types of issues addressed in simulation studies.

4. Verification and validation evidence can be collected

based on the underlying relationships.Some recent papers that use the factory physics approach

are [4549].

3 Modeling and analysis

The use of the factory physics concepts in a system dynamics

model may, at first glance, appear to be somewhat contradic-

tory. The factory physics approach as presented in Chapters

8 and 9 of Hopp and Spearman is based on long-run steady

state analysis of the production system, generally derived

using the methods of queuing analysis. System dynamics, on

the other hand, usually emphasizes the dynamic behavior of

complex systems that are not in steady state. However, for our

objective in this paper, the factory physics equations provide a

systematic mathematical model linking the mean and variance

of key system parameters such as setup and repair times to key

performance measure such as cycle time and utilization. In

order to use these equations as the basis for a system dynamics

model, we assume that the time increments that form the basis

of the system dynamics model are quite long, corresponding

to periods of the order of several months. This is a reasonable

assumption in our context, since it generally takes some time

to identify opportunities for improvements, implement the

necessary changes and obtain the results. We thus assume that

within each time period, the queue representing the manufac-

turing system will be in steady state, allowing us to use the

factory physics equations to describe the behavior of the

system. The assumption of long time periods also allows us toneglect the transient behavior at the boundaries between time

periods.

Our basic approach then is to model the performance of

the system over an extended time horizon of several years

using time increments of the order of several months.

Continuous improvement policies are modeled as a reduc-

tion in the mean or variance of the parameters studied

(arrival variability, process variability, quality, time to

failure, repair time, and setup time) obtained in each period.

In each period, the new parameter values are calculated

based on the improvements implemented in the previous

period, and the factory physics equations are used topropagate the effects of these improvements to system

performance measures. We assume a completely determin-

istic model of the effects of continuous improvement on

average cycle time, following the suggestion of Sterman

[36] that a deterministic approach is generally sufficient to

capture the principal relationships of interest. Note that the

effects of randomness in the operation of the system itself

are captured by the variances used in the factory physics

equations, and our primary performance measure is the

expected cycle time of the system in each period.

Surprisingly, given the extensive discussion of continuous

improvement and cycle time reduction in the literature and

industry, there seems to be very little industrial data available

on the rates of improvement realized over time in different

industries, which makes it difficult to calibrate models of this

type. Hence, we demonstrate the behavior of our model

through a simplified example of our own construction.

3.1 The model

We consider a manufacturing system modeled as a single

server with arbitrary interarrival and processing time distribu-

tions, which we shall represent as a G/G/1 queue. The

notations and relations used in the model are as follows:

t0=>mean natural processing time (the time required to

process a job without any detractors other than the

variability natural to the production process);

0=>standard deviation of the natural processing time;

te=>mean effective time to process one good part

(which is the natural processing time modified by the

impacts of disruptions such as setups and machine

failures);



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ce=>coefficient of variation of the effective time to

process one good part;

L=>average lot size;

ta=>mean interarrival time between lots;

ca=>coefficient of variation of the mean interarrival

time between lots;

l=>arrival rate of lots (the inverse of time between

arrivals, giving l=1/ta);D=>mean annual demand

H=>total number of hours worked in a year.

As the system must be in steady state to avoid

unbounded accumulation of jobs in the queue, the mean

arrival rate to the system must equal the mean demand rate,

implying ta=LH/D.

The mean time to process a lot of L parts is then given

by Lte, and the mean utilization of the server by:

uLte

ta

Dte

H1

The other primary performance measure of interest in

this study is the mean cycle time. For the G/G/1 queue, no

exact analytical expression exists, but the following

approximation has been found to work well and is

recommended by Hopp and Spearman [1]:

CTc2a c

2e

2

u

1 u

Lte Lte 2

where LTe is the mean time to process one lot.

The average work in process is given by the well known

Littles Law [1]:

WIP l CT L 3

The effective time to make one piece is constructed from

the natural processing time by adding in first the effects of

preemptive disruptions, in our case machine failures, then

the effects of non-preemptive outages, in our case setups;

and finally the effect of defective items. Both the means and

the variances of the effective processing times must be

calculated, as reflected in the model. Thus we first calculate

the mean and variance of the intermediate effective process-

ing time with machine failures, which we shall denote as tfe .

Following Hopp and Spearmans treatment, we shall assume

that the time between failures is exponentially distributedwith mean mf, and that the time to repair has mean mr and

variance s2r. Then the mean availability of the server is

given by A mf= mf mr

, yielding tfe t0=A, and

sfe

2

s20

A2

m2r s2r

1 A t0

Amr4

We now incorporate the effects of setups, assuming, as in

Hopp and Spearman [1], that a setup is equally likely after

any part is processed, with expected number of parts

between setups equal to the specified lot size L. The mean

setup time is denoted by ts, and its variance by s2

s. We thus

obtain the mean of the effective processing time with both

non-preemptive and preemptive outages (denoted by teo)as

toe tfe ts=L. Its variance is given by:

soe

2 sfe

2

s2

s

L

L 1

L2

t2s 5

Finally, incorporating the effect of defective items, we

have the overall mean of the effective processing time te,

given by te toe= 1 p , where p denotes the proportion of

defective items. The overall variance of the effective

processing time is given by:

s2e

soe

21 p

p toe 2

1 p 26

Figure 2 shows all of these relationships in a stock and

flow diagram.

Since our objective is to examine the effects ofcontinuous improvement in six parameters on the cycle

time of the system over time, we need a mechanism to

model continuous improvements. We use an exponential

model of improvement, where the value of a parameterA at

time t is given by:

At A0 G et=t 7

where, A0 denotes the initial value of the parameter, and G

the minimum level to which it can be reduced. The

parameter represents the average amount of time it takes

for the improvement to be realized, representing in our case

the difficulty of improving the parameter in question.Figure 3 shows the SD structures used to model improve-

ment on mean setup time. This structure is linked to the

variable setup time with improvement in Fig. 2. Similar

structures are used to model the improvements in the other

parameters studied (arrival variability, process variability,

setup time variability, repair time variability, and natural

process time variability), quality, mean time to failure, and

repair time. These structures are linked to the following

variables, respectively: arrival coefficient of variation with

improvement, variance of setup time with improvement,

variance of repair time with improvement, variance of

natural process time with improvement, defect rate with

improvement, mean time to failure with improvement, and

repair time with improvement.

3.2 Parameters of the model

We will vary individual parameters in different experiments

to examine their effect on the relationship between lot sizes

and cycle times. The basic time period in the system

dynamics model is assumed to be 3 months or 12 weeks.



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This is a reasonable time increment for the purposes of this

paper, since it is likely to require several months to develop

and implement the improvements needed to make a

significant reduction in repair or setup times. We simulate

the operation of the system over a period of 10 years, or 40

quarters. Since our objective is to study the effects of

continuous improvement in system parameters, the annual

demand is held constant at D=11,520 parts/year. We

assume an initial lot size of 200 parts, and that the plant

operates a total of H=1,920 h/year. The interarrival times

are assumed to be exponentially distributed (ca=1), as is the

natural processing time per part, with t0=6 min and c0=1.

At the start of the simulation, the mean time between

failures mf=9,600 min, the mean time to repair is mr=

480 min, and the mean setup time is ts=180 min. The

parameter of the improvement process was chosen to

provide a half life for the exponential decay of 1 year. The

initial proportion of defective items p=5%.

We vary the lot size in order to examine the effect of lot

sizes on cycle time. This is done for all improvement

policies tested: (1) no improvement, (2) 50% improvement

in arrival variability, (3) 50% improvement in each of the

parameters affecting process variability (natural process

variability, repair time variability and setup time variabil-

ity), (4) 50% reduction in defect rate, (5) 50% increase in

mean time between failures, (6) 50% improvement in mean

repair time, (7) 50% improvement on setup time, (8) 5%

improvement in all variables, (9) 10% improvement in all

variables, (10) 15% improvement in all variables, and (11)

20% improvement in all variables.

4 Results

Figure 4 shows the effect on expected cycle time of all 50%

improvements over the time period (cases (1) to (7)) for a

lot size of 200 parts. Similar figures can be drawn for the

Set up Time with

improvement

Improvement

on set up time

Error on set up time

improvement

GOAL REGARDING SETUP TIME

IMPROVEMENT

Improvement rate onset up time

ADJUSTMENT TIME FORSET UP TIME

IMPROVEMENT

-

+

B2

VARIANCE OF

SET UP TIME

Fig. 3 SD Structure of improvement in setup time

arrival rate throughput

Utilization

Set up Time with

improvement Arrival coefficient ofvariation withimprovement

Coefficient of variation for

effective processing time

Lot Size

NATURAL

PROCESS TIME

TIME WORKED

DURING THE YEARANNUAL

DEMAND

Number of pieces on

queue

Queue Time

Cycle Time

Variance of of effective processingtime with nonpreemptive and

preemptive outages

Mean repair time with

improvement

Availability

Mean of effective processingtime with nonpreemptive and

preemptive outages

Variance of set up time

with improvement

Variance of effective processingwith preemptive outage

(machine failures)Variance of natural

process time withimprovement

Total WIP

Variance of repair time

with improvement

Defect Rate withimprovement

Mean time to failure

with improvement

production rate

Overall mean ofeffective processing

time

Overall variance of

effective processing time

Fig. 2 Main body of the SD model



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other lot size values tested (600, 400, 170, 150, 130, 100, 80,

70, 60, 40, 30). From these results, lot size-cycle time curves

are drawn for each improvement policy after these curves

become stable. The resulting lot size-cycle time curves for the

large improvement program are discussed in Section 4.1. The

same procedure is performed for the small improvement

program and reported in Section 4.2.

4.1 Effect of large improvements in just one variable on lot

size x cycle time relationship

Figures 5, 6, 7, 8, 9, and 10 present the effects of each of

the six 50% improvement programs (cases (2) to (7)) on the

lot size-cycle time relationship, while Fig. 11 presents all

the effects in a single graph for comparison. Table 2

presents the values used to build Figures 5, 6, 7, 8, 9, 10,

and 11. In these figures, it can be seen that:

50% improvement in arrival cv has only slight effect on

cycle time reduction for given lot size. This effect is

even shorter when lot sizes are decreased. This may be

because of the fact we are considering a single

workstation.

As expected, a 50% improvement in defect rate, repair

time, time to failure, setup time, and process variability

shift the lot size-cycle time curve down and to the left,

reducing the lot size required to achieve a given cycle

time.

The positive effect on cycle time of 50% improvement

in setup time, process variability and defect rate

Graph for Cycle Time600

500

400

300

2000 30 60 90 120

Time (months)

Improvement in Process variabilityImprovement in Arrival cv

Improvement in Time to failureImprovement in defect rateImprovement in repair time

No improvement

Improvement in set up time

Fig. 4 Cycle time performance of all 50% improvements over time for a lot size of 200 parts

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

CycleTime(hours)

Lot Size (pieces)

no improvement

improvement in arrival cv

Fig. 5 The effect of 50% improvements in arrival cv on lot size-cycle

time curve

0

500

1000

1500

2000

25003000

3500

4000

0 100 200 300 400 500 600 700

Lot Size (pieces)

CycleTime(hou

rs)

no improvement

improvement in process

variability

Fig. 6 The effect of 50% improvements in process variability on lot

size-cycle time curve



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increases as lot sizes are reduced. This suggests a

strong interaction effect between lot sizes, cycle time,

and improvement in system parameters. In particular,

this indicates the presence of a virtuous cycle time:

improvements in setup time, defect rate, and process

variability allow the reduction of lot sizes, which

allows reduction of cycle times beyond the level that

would be achieved by improving the system but

keeping lot sizes constant. Thus, the small lot sizes

advocated by lean manufacturing are a result of

continuous improvement efforts; reduction of lot sizes

without any accompanying improvement in shop floor

capabilities will merely increase cycle time, as sug-

gested by Fig. 1. The cycle time reductions from 50%

improvement in repair time and time to failure increase

at extreme values of the lot sizes. This is to be

expected; the effect of these parameters is to make

more capacity available.

50% improvement in setup time achieves the best cycle

time reduction for small lot sizes. Improvement in

setup time is the only improvement that allows

production system to use really small lot sizes (e.g.,

30 or 40 parts);

On the other hand, the importance of lot sizes to

effective manufacturing performance is also evident from

the results. Table 2 shows that in the original system with

no improvements, a lot size of 150 parts leads to an

average cycle time of 530 min. Reducing the lot size to 80

leads to significantly higher cycle time even when all

improvements have taken place. Thus, a poor choice of lot

sizes can completely negate the benefits of a significant CI

program.

4.2 Effect of small improvements in several variables on lot

sizecycle time relationship

Figures 12, 13, 14, and 15 present comparisons between

50% improvement in set up time, no improvement and each

of the small improvement programs in all parameters

simultaneously (5%, 10%, 15%, or 20%). Figure 16

presents a comparison between the two large improvements

that achieves the best results in the last section (set up time

and process variability) and the small (5%, 10%, 15% or

20%) improvement in all parameters simultaneously. The

numerical values corresponding to this figure are shown in

Table 3. A 15% simultaneous improvement in all variables

outperforms all the large individual improvements, except

when very small lot sizes are used. Large improvements in

setup time achieve the best result in this case.

In Fig. 16, the curves for 50% improvement in setup

time and process variability represent situations where a

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

Lot Size (pieces)

CycleTime(hours)

no improvement

improvement in

defect rate

Fig. 7 The effect of 50% improvements in defect rate on lot size

cycle time curve

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

Lot Size (pieces)

CycleTime(hou

rs) no improvement

improvement in time tofailure

Fig. 8 The effect of 50% improvements in mean time between

failures on lot sizecycle time curve

0

500

1000

1500

2000

25003000

3500

4000

0 100 200 300 400 500 600 700

Lot Size (pieces)

CycleTime(hou

rs)

no improvement

improvement inset

up time

Fig. 10 The effect of 50% improvement in mean set up time on lot

sizecycle time curve

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

Lot Size (pieces)

CycleTime(hours)

no improvement

improvement in

repair time

Fig. 9 The effect of 50% improvement in mean repair time on lot

sizecycle time curve



9/13

major reduction in these parameters is obtained. An

improvement of this magnitude would very probably

require the adoption of new technology, or at least a

sustained, focused engineering effort. However, the curves

for 10% and 15% improvement in all parameters capture

almost the entire cycle time benefit of these programs,

except at small lot sizes. Even a 5% improvement in all

parameters yields a 50% improvement in average cycle

time at small lot sizes over the no improvement situation.

As suggested by the successful approach of Toyota,

investing in small, combined improvements in all shop

floor parameters yields better cycle time reduction than a

single large, high-investment improvement. Examination of

the Kingman equation relating cycle time to manufacturing

parameters suggests the reason for this. The benefit of

reduction in any given parameter may not be great in itself,

but the benefits tend to be multiplicative, and hencemutually reinforcing. In system dynamics terminology, this

suggests positive feedback between improvements in the

different parameters, which is good news for managers.

However, the opposite is also trueif the values of several

parameters begin to deteriorate simultaneously, the detri-

mental effects will also be mutually reinforcing, leading to

precipitate degradation in cycle time.

5 Conclusions

In this paper, a combination of the SD and factory physicsapproaches is used to study the effect of continuous

improvement programs aimed at improving six key parame-

ters (arrival variability, process variability, quality (defect

rate), time to failure, repair time, and setup time) on lot size-

cycle time relationship in a multi-product, single-machine

environment. Two sets of experiments were performed: (a) a

large (50%) improvement in each parameter separately, as

might be obtained by a significant one-time investment; (b) a

small improvement in all parameters simultaneously.

There are two salient conclusions from this set of

simulation experiments. The first of these is the strong

interaction between improvements in different system param-

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

No

improvement

Improvement

in set up

Improvement

in defect rate

Improvement

in arrival cv

Improvement

in repair time

Improvement

in time to

failureImprovement

in process

variability

Lot Size (pieces)

Cycle

Time(hours)

Fig. 11 Effect of 50% improvements on the lot size-cycle time curve

Table 2 Values of lot size-cycle time curve for all improvement programs

Lot size Cycle time

No improvement Improvement

in arrival cv

Improvement

in process cv

Improvement

in defect rate

Improvement in

time to failure

Improvement

in repair time

Improvement

in set up time

600 896.77 837.47 594.18 825.86 705.73 673.92 784.69

400 696.97 653.37 459.69 639.08 559.47 535.64 574.68

200 535.56 505.91 349.69 483.19 446.19 428.72 373.03

170 527.18 498.9 343.29 472.19 442.64 425.39 345.68

150 530.01 502.25 344.38 471.24 447.33 429.8 328.74

130 545.95 518.13 353.84 479.99 462.89 444.36 313.53

100 633.81 602.98 408.81 537.91 538.01 514.1 297.13

80 860.67 820.17 552.77 681.52 717.56 677.58 296.24

70 1,244.88 1,187.22 797.44 890.84 996.97 923.86 303.14

60 3,735.17 3,564.47 2,385.17 1,660.44 2,329.88 1,979.78 321.05

40 501.39

30 2,205.09



10/13

eters and improved cycle time. While improvements in system

parameters provide cycle time benefits on their own, furtherbenefits can be realized by reducing lot sizes to the levels

permitted by the improvements. Similarly, when a firm sets its

lot size near the minimal value on the lot sizecycle time

curve, the need for improvement in machine availability

decreases. In other words, a good choice of lot size can offset

the disadvantages of unreliable equipment to some degree,

although clearly the firm should continue to improve its

equipment reliability. Similarly, when the lot sizes are small

and hence utilization is high, improved machine up time

creates additional capacity, reducing utilization and allowing

significant reduction in cycle time.

This close interaction between lot sizes and system

parameters has another implication. As seen in any of the

figures above, simply reducing the lot sizes without any

improvement in the system parameters may lead to a

catastrophic increase in cycle time. If the lot sizes were

extremely high to begin with, quite significant reductionsmay be possible with significant cycle time benefits,

essentially moving to the left along the linear portion of

the lot sizecycle time curve. Since very few manufacturing

facilities can predict the shape of the lot sizecycle time

curve with any degree of precision without a significant

data collection and analysis effort, this suggests that

management exercise considerable caution when reducing

lot sizes. A gradual reduction over time, making sure that

enough time has elapsed for the effects of each reduction to

be observed and understood, is probably the best strategy. It

is better to gradually reduce lot sizes than to reduce them to

such a degree that setups consume an undue amount of

capacity and compromise the performance of the system.

Our results in Table 2 show that a poor choice of lot sizes

can offset all the benefits of a major CI program.

0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800

CycleTim

e(hours)

Lot Size (pieces)

no improvement

10% improvement in all

variables

50% improvement in set up

time

Fig. 13 Comparison between 50% improvement in set up time, 10%

improvement in all variables and no improvement case

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

CycleTim

e(hours)

Lot Size (pieces)

no improvement

20% improvement in allvariables


time



0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800

CycleTime(hours)

Lot Size (pieces)

no improvement


50% improvement in set uptime



0

500

1000

1500

2000

2500

3000

3500

4000

0 200 400 600 800

Cycle

Time(hours)

Lot Size (pieces)

no improvement



time





11/13

The conclusion, again, is inescapable: improving the

parameters of the shop floor is beneficial in itself, but when

combined with the right choice of lot size the benefits are

significantly enhanced. This result supports the Quick

Response Manufacturing theory, which claims that in an

environment with considerable set up time, a lot size of one

piece, contrary to what is advocated by Lean Manufactur-

ing, actually contributes to increased cycle time. Put

another way, the lot size of one advocated in the Lean

Manufacturing literature requires signifciant improvements

in the parameters of the produciton system itself if it is to be

realized without compromising cycle time performance.

Our second salient finding is that a significant proportionof the benefits obtained by a major improvement in one

parameter, as might be achieve by investing in a new

technology, say, can be obtained by pursuing small

improvements in multiple system parameters simultaneous-

ly over time. As expected, setup time reduction allows the

system to operate with the smallest lot size (in our case for

30 or 40 parts). However, such a dramatic improvement

may be difficult to achieve without major capital expendi-

ture and interruptions to production. Our results suggest

that a substantial portion of the benefits of this type of

dramatic reduction in setup time can be improved by

relatively minor simultaneous improvements in otherparameters, which can be pursued in parallel with a longer

term setup reduction effort. Even a 5% improvement in all

parameters gives cycle time savings of almost 50% at low

lot sizes.

The results presented underscore the benefits of the

factory physics approach to understanding and diagnosing

manufacturing systems. As the factory physics equations

suggest, the behavior of these systems over time is quite

nonlinear; the effects of changes in parameters are

multiplied to yield nonlinear improvements or degradations

in cycle time. The presence of positive feedback between

improvements in system parameters, lot sizes, and cycle

time goes a long way towards explaining how Japanese

Table 3 Values of lot size-cycle time curve used to build Fig. 12

lot

size

Cycle time

No improvement 5% Improvement

in all variables

10% Improvement

in all variables

15% Improvement

in all variables

20% Improvement

in all variables

50% Improvement

in set up

50% improvement

in process cv

600 896.77 776.4 672.05 581.27 502.12 784.69 594.18

400 696.97 601.96 519.72 448.27 386.05 574.68 459.69

200 535.56 457.23 390.34 332.94 283.5 373.03 349.69170 527.18 447.46 379.95 322.43 273.22 345.68 343.29

150 530.01 446.13 377.56 318.77 268.82 328.74 344.38

130 545.95 456.19 381.95 320 267.95 313.53 353.84

100 633.81 513.44 418.69 342.83 281.3 297.13 408.81

80 860.67 654.91 508.69 400.53 318.16 296.24 552.77

70 1,244.88 863.25 629.57 473.5 363.17 303.14 797.44

60 3,735.17 1,656.39 985.35 657.72 466.07 321.05 2,385.17

40 501.39

30 2,205.09

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

No improvement 5% improvement in allvariables


variables


variables


50% Improvement in set up

50% improvement inprocess variability

Lot Size (pieces)

CycleTime(hours)

Fig. 16 Comparison between the large improvement in setup and

process variabilities and simultaneous small improvements in all

variables



12/13

factories have been able to achieve the massive cycle time

and WIP reductions that many Western experts simply

could not believe were possible in the early 1980s.

Finally, the SD/Factory Physics combined model pro-

posed in this paper has been shown to be a valuable tool for

simulating the impact of alternative continuous improve-

ment programs on manufacturing performance measures

over time.A number of extensions of this approach suggest

themselves. An interesting direction is to provide insight

into the allocation of limited continuous improvement

resources in a complex systemshould all available

resources be directed towards improving one specific

resource, or should parallel efforts be maintained in several

different areas? Another interesting question is how the

benefits of different CI programs are affected by uncertainty

in ability to achieve improvements. One would conjecture

that a portfolio approach, where multiple improvements are

pursued simultaneously, would yield better average im-

provement over a given time interval than an effortdedicated at a single highly uncertain improvement.

Acknowledgments The research of Reha Uzsoy was partially

supported by the National Science Foundation under Grant No.DMI-

0559136. Moacir Godinho Filho would like to acknowledge FAPESP

Brazilian agency for funding this research.

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