the impact of lot-sizing on net profits and cycle times in the n-job, m-machine job shop with both...

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doi:10.1016/j.ijp

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(B.D. Neureuth

Int. J. Production Economics 97 (2005) 263–278

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The impact of lot-sizing on net profits and cycle times in then-job, m-machine job shop with both discrete and

batch processing

George Kenyona,�, Cem Canelb, Brian D. Neureutherc

aDepartment of Management and Marketing, College of Business, Lamar University, Beaumont, TX 77710, USAbDepartment of Information Systems and Operations Management, Cameron School of Business,

University of North Carolina at Wilmington, Wilmington, NC 28403-3297, USAcAnalytical Department, School of Business, Indiana State University, Terre Haute, IN 47809, USA

Received 1 June 2003; accepted 1 July 2004

Abstract

One of the key factors for productivity growth in the semiconductor industry is the improvement in overall

equipment effectiveness (OEE). In order for the industry to meet its future goals it must find methods to continuously

improve its OEE. This study assesses the impact that lot sizes can have on the operational variables that most influence

OEE, net profits, cycle-time, throughput, work-in-process, and operating expenses. In a multiple operation system,

where both discrete and batch processing is utilized, the interactions among products, product lot sizes, and equipment

load capacity affect the arrival and service rates of all operations. As a result, cycle time and its components,

throughput and work-in-process, are affected. This study shows that progressively smaller lot sizes do not provide

continuous improvements in cycle time, throughput, work-in-process inventories, operating expenses, or net profits.

Furthermore, we show that the impact of lot sizes on cycle times is not significantly related to setup times.

r 2004 Elsevier B.V. All rights reserved.

Keywords: Analytic models; Cycle-times; Simulation

1. Introduction

Historically, the semiconductor industry hasmaintained a steady 25 to 30 percent productivity

e front matter r 2004 Elsevier B.V. All rights reserve

e.2004.07.007

ng author.

sses: [email protected] (G. Kenyon),

du (C. Canel), [email protected]

er).

growth per year, as measured in the reduction ofwafer production cost per function (SIA, 1997).This growth has occurred despite the escalatingfactory costs of approximately 20 percent per year(SIA, 1997). Due to diminishing annual gains inyield and wafer size, there is a greater emphasisbeing placed upon factory productivity. A keyelement in the strategy to remain on its historicimprovement curve is the continuous improvement

d.

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G. Kenyon et al. / Int. J. Production Economics 97 (2005) 263–278264

in operating expenses per centimeter square ofwafer production.

The Semiconductor Industries Association(SIA) recognizes that in order to meet its futuregoals, improvements are needed in developing,purchasing and operating equipment and reduc-tions in feature size, and increases in waferdiameter are no longer sufficient. Improvementsin this area are measured in overall equipmenteffectiveness (OEE). Overall equipment effective-ness is a measure that can lead to improvements innet profit and in cost reduction. OEE can beimproved by eliminating what has been termed thesix big losses of a production setting (Nakajima,1998). These include losses from (1) poor produc-tivity and lost yield due to poor quality, (2) setupand adjustment for product mix change, (3)production losses when temporary malfunctionsoccur, (4) differences in equipment design speedand actual operating speed, (5) defects caused bymalfunctioning equipment, and (6) start up andyield losses at the early stage of production.

In support of OEE improvement, some complexjob shop industries, such as the semiconductorindustry, have realized that greater emphasis mustbe placed on factory productivity (due to dimin-ishing annual gains in yield and wafer size).According to the SIA (1997), these OEE measure-ments are complementary to cost-of-ownershipand throughput measurements. The SIA (1997)also has recognized that in order to exceed the 65percent OEE barrier, improvements in factoryplanning and scheduling, and better modelingtools for assessing and optimizing capacity areneeded. This has led the semiconductor industry toseek new ways to get more productivity from itsfab investments by developing equipment andprocesses that improves the economics of produc-tion (Douglas, 1999).

Throughout most of this century, firms pro-duced finished goods that were stored in inventoryuntil they were sold to the customers. In thecurrent business environment, where speed andflexibility are key competitive factors, maintaininglarge inventories is unacceptable. The currenttrend in manufacturing has been to migrate fromproduce-to-stock strategies to produce-to-orderand engineer-to-order strategies that curtail over-

head costs, especially for finished inventory. Inorder to support organizational goals, operationsmanagers have to decide how to minimize productcycle times and maximize net profits.

As competition in the global marketplaceincreases and customers continuously demand forhigher quality levels and shorter cycle times,management’s decisions must focus upon quality,speed, flexibility, revenue generation, and costreduction. Buffa (1984) stated that day-to-dayoperating decisions, such as lot sizing, have majorstrategic implications for the firm. Thus, optimallysized production lots can help meet these strategicneeds. This study assesses the impacts that lot sizesand material release rates can have on net profitsand cycle times, as well as, the operationalvariables that most influence them: throughput,work-in-process, and operating expenses. Further-more, this study shows that contrary to conven-tional wisdom; setups are not the principle driverof production cycle time in the multiple product,multiple operation job shop, and that progres-sively smaller lot sizes do not assure cycle time orcost improvements. The next section provides anoverview of the literature in this area. Section threepresents an analytical model that has the objectiveof maximizing net profits through selection of anoptimal lot size for each product. Section fourdescribes the experiment, section five provides ananalysis of the results, and section six presents theconclusions.

2. Literature review

There have been extensive studies on issuesrelated to lot sizing since lot sizing is affected byseveral operations decisions, and capacity plan-ning decisions are affected by lot sizing decisions.Karimi et al. (2003) present an extensive survey onsingle-level lot sizing problems, their variants, andexact and heuristic solution approaches. Drexland Kimms (1997) provide a survey for thecapacitated, dynamic, and deterministic lot sizingproblems, where continuous time models andmulti-level lot sizing and scheduling are discussed.Ramasesh et al. (2000) present an economicproduction lot size model that minimizes the total

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G. Kenyon et al. / Int. J. Production Economics 97 (2005) 263–278 265

cost when a production lot is split into smaller sub-lots.

Bogascheusky et al. (2001) describe a multi-stage production model where lot size is uniformin all stages with a single setup and no interruptionat each stage. They develop an optimizationmethod that determines the economic lot size withset up, inventory holding and transportation costs.Aksen et al. (2003) provide a different version ofthe Wagner–Whitin model for the deterministic,uncapacitated single-item lot sizing problem withlost sales where the objective is to maximizeprofits. Dellaert and Jeunet (2003) state that theperformance of multi-level lot sizing problemsimproves in a rolling schedule environment. Jaberand Bonney (2001, 2003) investigate the effects oflearning and forgetting in setups and productquality on lot sizing problems.

Chung (2003) investigates the production lotsizing problem with machine break downs andprovides approximations to the optimal lot size.Jain et al. (2003) develop a generalized stochasticPetri net model that captures factors such as reentrant processing, machine failures, and loadingas they pertain to wafer fabrication. In their studythey develop a simulated annealing-based schedul-ing strategy using mean cycle time and tardiness asperformance measures to obtain efficient androbust schedule for a known hard problem.

The literature suggests that long productionruns are not efficient, and that sub-batching withoperational overlap can improve manufacturingcycle times. Spence and Porteus (1987) show that,once the production system expands into a multi-ple operation system, the EOQ framework nolonger applies. With the multiple operation pro-duction system, the demands placed upon up-stream resources by the downstream resources areno longer stationary over time, but will dependupon lot size and scheduling. In the multipleoperation production system, interactions betweenthe product’s lot size and the server’s capacity willaffect the arrival and service rates of all opera-tions, and therefore affect cycle time and itscomponents, throughput and work-in-process.

Karmarkar et al. (1985) point out that it isconventionally assumed that at the operationallevel, the dynamic performance of job shops with

queues and delays are primarily controlled bysequencing and dispatching at machines. It isknown that a major determinant of queuingbehavior is the lot sizing policy employed, andintuitively, by reducing lot sizes the problem oflarge queues and delays can be reduced. Karmar-kar et al. (1985) show that reductions in lot sizeswill only ameliorate the queuing problems at first,but eventually cause the total workload atmachines to increase because of the increasednumber of setups.

Several articles relating to environments thatmimic similar behavior as complex job shopspresent other uses of OEE. Ki-Young and Phillips(2001) discuss a loss classification scheme forcomputing OEE for capital extensive industrieswhile Dal et al. (2000) discuss a practical analysisof operational performance measurement at Air-bags International. They determine that the use ofthe OEE measure is an effective measure withinthe operational environment and describe severalbenefits from using OEE as an operationalmeasure.

However, a logical question then arises. What isthe impact that material scheduling (i.e., lot sizeand material release rates) have on net profits andcycle times, and on the operational variables thatmost influence them: throughput, work-in-processinventory levels, and operating expenses? Weaddress this question by developing a simulationmodel that utilizes one of the most complex jobshop environments that exists, a semiconductormanufacturing environment. We examine im-provements in OEE based on lot sizes, releaserates, and bottleneck location decisions.

3. The analytic model

In order to investigate the impact of materialscheduling on job shop productivity and netprofits, it is necessary to first present a model thatfacilitates the maximization of the firm’s netprofits through the selection of an optimal lot sizefor each product produced. We contend thatoptimally sized production lots can increasethroughput while simultaneously decreasing oper-ating expenses.

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According to Goldratt (1990), the maximizationof net profits is accomplished by increasingthroughput, while simultaneously decreasing oper-ating expenses. Goldratt defines several terms thatdescribe the measurement of the productionprocess as follows:

�
Throughput is defined as ‘‘the rate at which thesystem generates money through sales.’’Throughput is measured as gross revenues lessraw materials cost. Due to the probability ofscrap in the process, and to ensure that all rawmaterials are accounted for, the deduction forraw materials is made in the production costconstruct.
�
Operating expense is defined as ‘‘all the moneythe system spends in turning inventory intothroughput.’’
�
Net profits are defined as ‘‘simply throughput(gross revenues) minus operating expense.’’ Thisrelationship can be expressed in the followingform (Goldratt, 1990):
NP ¼Xk

j¼1

Tj �Xk

j¼1

OEj ; (1)

where Tj is the sales in dollars for product j,and OEj the operating expense in dollars forproduct j.

As can be seen from the subscripts in Eq. (1),throughput and operating expenses are not in thesame units. Traditional cost accounting methodshave accounted for and defined overhead costs aspart of the operating expense. We define overheadcosts, or overhead as indirect expenses by pro-ducts.

By converting operating expenses into its twobasic cost categories, production costs (P) andoverhead costs (H), and using gross revenues (R)in place of throughput, net profits (NP) can bemodeled as

NP ¼Xk

j¼1

Rj �Xk

j¼1

Pj þXk

j¼1

Hj

" #; (2)

NP ¼Xk

j¼1

½Rj � Pj � Hj�;

where Rj is the gross revenue in dollars forproduct j, Pj the production costs in dollarsfor product j, and Hj the overhead costs in dollarsfor product j.

The assumptions for the analytic model are asfollows:

1.
Production units are discrete. 2. The sequencing of operation for each product
routed through the wafer fab is unique to thatproduct type.

3.
All units within a lot are processed simulta-neously where possible. Should a lot need to besplit into multiple runs, due to machine loadcapacity constraints, no units from other lotswill be mixed into these runs.
4.
Lots are moved between processing operationsupon completion of current operation.
5.
No operation shall have mixed product types. 6. Operations may alternate between product
types based upon a first come, first servedqueuing policy.

7.
Processing times, setup requirements, andprocessing/machine capacities may differ ateach operational step.
8.
The load capacity of each machine in the waferfab is fixed. The number of units/lots loadedshall depend upon recipe processing require-ments.
9.
No buffer limits on work-in-process areallowed at any operation.
10.
Labor costs are divided into two categories:operating expense and overhead expense.
11.
The time to market for the simulated waferfab is assumed to be equal to that of theindustry.
12.
Due to the production data collected from amajor semiconductor manufacturer (hence-forth refereed to as ‘‘SM’’), not being allocateddown to the device type level, and because ofthe similarity of processing, device level costswere apportioned based upon the number ofoperations performed.
The objective of our research is to investigatethe impact of materials scheduling on job shopperformance and net profits, and to present amodel that facilitates the maximization of a firm’s

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net profits through the selection of an optimal lotsize for each product produced. We contend thatoptimally sized production lots can increasethroughput while simultaneously decreasing oper-ating expenses. Subject to the constraints placedupon the preceding constructs, the model forcalculating net profits for a given time period isdenoted as (Kenyon, 1997):

MaxfNPg ¼ MaxXk

j¼1

ðRj � Pj � HjÞ

( ); (3)

where

Rj ¼ TjMj eaj ðl̄j�lj Þ=lj Þh i

; j ¼ 1; . . . ; k; (4)

Tj ¼ Y jDj

ZbjQj

Cbj

� s:t: Tjpmax system output

if Dj5max system output;

then Dj

ZbjQj

Cbj

� ffi Dj ; j ¼ 1; . . . ; k; ð5Þ

Pj ¼Tj

Y j

mj þXn

i¼1

Cij þ Lij

QjZi

þ Sij

!" #;

j ¼ 1; . . . ; k; ð6Þ

Hj ¼ Pj

Qj

cj

!bj þ yj

!; j ¼ 1; . . . ; k: (7)

In the above formulations, Eq. (3) is the netprofit maximization expression. Eq. (4) providesan expression for the calculation of expectedrevenues, Rj. With any given product j the revenueis based upon the throughput for some givenperiod of time and the average market price overthat time period. In a highly competitive market-place there can be a price premium for being firstin the market with a product, and this premium isa function of the time differential between thisproduct’s introduction and the next competitor’sintroduction of a similar product.

Eq. (5) provides an expression for calculatingthe system’s throughput, Tj. Every machine has adesign capacity such that the throughput for thatmachine is maximized by fully utilizing thatcapacity. The machine’s throughput is furtherreduced by its yield of good product. Furthermore,

the throughput of a process is metered by itsbottlenecking operation. Thus, the expectedthroughput of a production process at any giventime can be defined by the average utilization andyield of its bottlenecking resource.

Eq. (6) provides an expression for the calcula-tion of production costs Pj. The production costfor each product is the per unit raw material costand the sum of the processing costs (inclusive ofthe cost of all consumables, labor, and setups) ateach operation in the process divided by theaverage number of units processed per respectiveoperation. The total production cost for a givenproduct over a specific period of time is theproduction cost per unit times the yield adjustedthroughput of the process.

Eq. (7) provides an expression for the calcula-tion of overhead costs Hj. Overhead costs aretypically comprised of two components, a fixedcomponent and a variable component. The vari-able component is most often tied to productioncosts through some allocation factor. By account-ing for operational decisions that impact theefficiencies of the production process (i.e. loadutilization of the equipment), overhead allocationscan be increased for products that are not beingprocessed efficiently. The notations for the aboveexpressions are defined in Table 1.

4. The experiment

The job shop environment used in this researchis found in a typical semiconductor wafer fabrica-tion center. This type of job shop employs bothserial and batch processing. A batch-processingmachine is defined as one that can process severallots of material simultaneously, while a serialprocessing machine processes each item in a lotindividually. Machines that do not support anytype of batch operations are referred to as serialmachines. The machines typically found in a waferfabrication center will hold more than one wafer ofmaterial, but will process the wafer(s) in either abatch or a serial processing mode.

Semiconductor wafer fabrication centers areusually designed around a process layout, wheresimilar type processing equipments are grouped

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Table 1

Notations used in the analytical model

aj Scaling constant for cycle time taken in relation

to the industry average cycle time.

Cij Consumables cost rate for operation i and

product j.

Dj Period demand for product j.

Hj Overhead costs for product j.

k Number of product types.

n Number of operations.

Lij Labor rate for operation i and product j.

Mj Market price for product j.

mj The per unit raw material cost for product j.

Pj Production costs for product j.

Qj Lot or batch size of product j.

Rj Revenues for the product j.

Sij Setup cost of operation i and product j.

Tj Expected system output for product j.

Yj Process yield rate or process quality for product

j.

bj Variable overhead cost scalar quality for

product j.

Zbj Average expected number of lots per

production run at bottleneck operation b and

product j.

Zi Average expected number of lots per

production run at operation i.

lj ¼Qjcbj

The cycle time of the firm for product j.

l̄j The industry average cycle time for product j.

yj Fixed portion of overhead costs for product j.

r Process utilization.

cbj Load capacity of bottleneck operation b and

product j.

cj Load capacity of product j.


into work centers, and each work center will havefrom one to n machines. Each product introducedinto this shop has a unique processing sequence, orrouting, which often includes multiple re-entranceflows to multiple work centers. Also, multipleproducts are typically produced simultaneously inmost wafer fabrication centers. The wafer fabrica-tion center being modeled by the simulation modelcontains 381 machines that are divided into sixtydifferent work areas. With typical contemporaryintegrated circuit designs, it is not unusual to havemore than 200 production operations performedin the fabrication of a given semiconductor device.

Production data were collected from one plantof a USA-based Semiconductor ManufacturingCompany (SM). This data consisted of operating

expenses for the 5 years from 1992 through 1996.This data included product flows, processing data,and equipment data. Due to the production costdata not being allocated down to the product level,a direct by product comparison between theproduction data and the simulation model is notpossible. In discussions with the SM, it wasdetermined that the processing/costs were fairlyhomogeneous across the products, the primarydifferences in the operating costs between productswere associated with the number of processingoperations performed for each product. Theprocessing information is found in the productflows data collected. From this operating expenseswere allocated across the products for each quarterbased upon activity. A regression analysis wasconducted to identify independent operationalvariables that could be utilized in predicting theoperational expenses for each product in each ofthe simulation runs. Utilizing the parameterestimates from this regression analysis, costs areextrapolated from the results of the simulation.

The independent variable of primary interest inthis analysis is lot size. By varying the lot sizes ofthe three products used in the simulation, changesin the dependent variables (operating expenses, netprofits, and cycle time) are investigated. Changesin the material release rates only magnified theresults from changes in lot size. The following lotsizes were chosen for this experiment: 48, 24, 12, 6,and 3 units per lot. The reasoning for the selectionof these lot sizes is that, prior to the first quarter of1993, the standard production lot size used at SMwas 48 wafers per lot. After the first quarter of1993, the standard lot size was changed to 24wafers per lot. The remaining three lot sizes aredetermined by reducing the previous lot size inhalf.

The starting premise of our research was that aslot size decreases, measures of performancerelative to the production process would improve.Some of the expected benefits are: cycle timewould decrease, work-in-process inventory levelswould decrease, overhead costs would decrease,and production costs would decrease. One furtherfocus of our research is to determine if there is alower limit to lot size reduction, below which nofurther benefits are gained.

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The SLAM II simulation software was utilizedin the development of a discrete event simulationmodel for the semiconductor facility of interest.Fig. 1 shows the basic flow path of work for aprototypical integrated circuit manufacturingplant. For a discussion of the generic event-processing logic as well as the methodology usedto create the simulation, see Pritsker (1995,Chapter 11). Because the FORTRAN side ofSLAM II provides greater speed and flexibility inmodeling complex processes, we decided to use thefaster and more robust FORTRAN interface,rather than the network interface that is availablein SLAM II.

Each lot of material to be released into theproduction system is defined using the followingattributes: (1) job start time, (2) due date, (3)current work center, (4) current processing code,(5) current operation number, (6) cumulativeprocess yield, (7) cumulative production costs, (8)cumulative setup time, and (9) device type. Otherjob attributes used are: (10) current row pointer,(11) current machine number, (12) current opera-tor number, (13) logout terminal number, (14)current batch array job pointer, and (15) previousbatch array job pointer. These lots pass through a

Fig. 1. The simulated integrated

simulated semiconductor facility where schedulingof six separate events take place, as shown inFig. 2. Fig. 2 further provides a generic materialflow for the work centers within the waferfabrication center plant and displays when opera-tor and machine resources will be busy during thismaterial flow. Each of the event types is a separateFORTRAN subroutine that is scheduled accord-ing to the processing recipes of each product.SLAM II controls the timing of execution for eachof these scheduled events.

Materials enter the work center queue as a resultof a raw material release into the shop, or becauseof a transfer routing from another work center. Asa machine resource is freed, the simulated operatorgoes to the work center queue and removes aproduct lot based upon (1) a first-come, first-served queue priority, and (2) what the previousproduct type was. The second criterion is modeledin since it was an actual practice in the SM’s waferfabrication center. If the machine’s load capacity isgreater than the lot size of the job selected, morelots are batched with the current lot; as long asthey are compatible with the first lot’s processingrequirements and the total batch size does notexceed the total machine load capacity.

circuit fabrication process.

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Fig. 2. Work center material flow and resource.


During the setup operation, the wafers thatcomprise the selected product lot are loaded intothe machine, and the processing recipe is electro-nically downloaded. Once the processing starts,the operator is free to perform other tasks at thework center. When processing is complete, thewafers remain inside the machine until an operatoris available to remove them. The logout queue isused to generate the random timing of theoperator response to an end-of-process condition.

After the lot is unloaded from the machine, it islogged out of the work center via a networkedmini-terminal located at each machine. When thelogout activity is completed and more processingrequirements remain, the lot is transferred to thenext work center and placed in its work centerqueue. When all processing requirements arecompleted, the lot is removed from the shop, andstatistics are collected on the costs and processingtimes of each lot.

4.1. Evaluation of the production data

As previously discussed, actual operating ex-penses were collected from SM, by calendarquarters starting with the first quarter of 1992through the last quarter of 1996. SM pooled theseexpenses into 16 different categories: materials,inventory deltas, cost adjustments, direct labor,indirect labor, benefits, supplies, repair andmaintenance, sundries, depreciation, lease, taxes,

occupancy, utilities, computer paper, and otherservices. These expense pools represented the totaloperating expenses incurred in each quarter of the 5year period between 1992 and 1996 at the SM waferfabrication center. An ANOVA analysis wasconducted on these data to ascertain if there wereany differences in the operating expenses due to thechange in lot sizes by SM in the first quarter of 1993(48 wafers per lot to 24 wafers per lot). To test thedata from SM, the following hypothesis is asserted:

Hypothesis 1.

Ho1: The operating expense pools at 48 units perlot are equal to the operating expense pools at 24units per lot, versus the alternative hypothesis,

Ha1: The operating expense pools at 48 units perlot are not all equal to the operating expense poolsat 24 units per lot.

To test Hypothesis 1, a statistical analysis isperformed on the quarterly data collected. Thefirst question of interest is to determine if there is adifference in the operating expenses associatedwith the two different lot sizes. An ANOVAprocedure is employed to compare the means ofthe production data at the two different lot sizes.The results of the ANOVA procedure are shown inTable 2. The threshold used for determination ifthere is a significant difference in a cost pool wasthe 5 percent level of significance. The term ‘‘5percent level of significance’’ is defined as the

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maximum level of probability at which a true nullhypothesis could be rejected (Conover, 1980).From these results it can be seen that, at the 5percent level of significance, seven out of thesixteen expense categories are significantly affectedby the change in lot size. At the 0.10 level, nine ofthe sixteen expense categories are significantlyaffected.

The second question of interest, with respect tothe data, is to determine if the costs can bepredicted using operational parameters such as lotsize, output, work-in-process, and cycle time. Toconduct this analysis, the data are converted intocosts per lot and costs per unit. The number of lotsfor a given quarter is determined by adding theend-of-period, work-in-process to the total systemoutput for the period, then dividing by thestandard lot size used for that period. Costs arethen divided by the number of lots to arrive atcosts per lot.

Table 3 shows the results of the regressionanalysis that was performed on the expensecategories, investigating the predictability of thesecosts based upon independent variables such as lotsize and cycle time. It can be seen from theadjusted R2 shown in Table 3, lot size and cycletime were both strong predictors of operatingexpenses. Furthermore, from the T tests, both lotsize and cycle times were strongly significant in

Table 2

ANOVA of SM quarterly operating expenses

Dep variable Ind variable R2 DF

Materials Lot size 0.1509 1

Inv. delta Lot size 0.05256 1

Adj. costs Lot size 0.00011 1

Dir. labor Lot size 0.00932 1

Ind. labor Lot size 0.41387 1

Benefits Lot size 0.48101 1

Supplies Lot size 0.39407 1

Repr & maint. Lot size 0.25093 1

Sundry Lot size 0.04231 1

Depreciation Lot size 0.13281 1

Lease Lot size 0.19716 1

Taxes Lot size 0.38746 1

Occupancy Lot size 0.09155 1

Utilities Lot size 0.19106 1

Comp. paper Lot size 0.21389 1

Services Lot size 0.02186 1

virtually all cases. Based upon these results, and areasonable understanding of the nature of eachcategory, the various expense categories weredivided into fixed and variable costs groups andan equation was developed for calculating thecosts in the simulation model.

4.2. Testing the simulation model

The design used for the discrete-event simula-tion model employed three product types at fivedifferent lot sizes, and four different materialrelease rates. Using a factorial design, a total of290 simulations are executed, resulting in eighthundred and seventy observation sets. Based uponthe actual cycle times’ range in the SM’s produc-tion data, for the testing of hypothesis, thesimulation observations are restricted to cycletimes that are less than 0.13 years. Due to thisrestriction, only three hundred and eight observa-tion sets are used in the following tests.

To test for changes in the production costs, thefollowing hypothesis is made:

Hypothesis 2.

Ho2: The production costs at the various lot sizesare all equal, versus the alternative hypothesis of,

Ha2: The production costs at the various lotsizes are not all equal.

ANOVA SS Mean sq. F val Pr4F

7.9387E+12 7.9387E+12 3.20 0.0905

2.6643E+12 2.6643E+12 1 0.3309

2.3632E+8 2.3632E+8 0.00 0.9653

7.3689E+9 7.3689E+9 0.17 0.6855

2.6774E+12 2.6774E+12 12.71 0.0022

1.2227E+12 1.2227E+12 16.68 0.0007

1.4688E+12 1.4688E+12 16.68 0.0007

5.8060E+11 5.806E+11 6.03 0.0245

1.3566E+10 1.3566E+10 0.80 0.3843

8.2561E+12 8.2561E+12 2.76 0.1142

1.4552E+9 1.4552E+9 4.42 0.0498

4.4476E+9 4.4476E+9 11.39 0.0034

7.4062E+9 7.4062E+9 1.81 0.1947

1.5853E+9 1.5853E+9 4.25 0.0540

1.3196E+8 1.3196E+8 4.90 0.0401

1.7507E+11 1.7507E+7 0.40 0.5338

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Table 3

Regression analysis of SM quarterly costs

Dependent variable Costs per lot Costs per unit

Adj. R2 Ind. variables Prob4T Adj. R2 Ind. variables Prob4T

Materials 0.9489 Lot size 0.0748 0.9350 Cycle time 0.0001

Cycle time 0.0052 Cycle time2 0.0001

Cycle time2 0.0002

Inv. delta 0.1848 Lot size 0.0273 0.0113 Intercept 0.1566

Cycle time 0.0380 Cycle time 0.1556

Cycle time2 0.1570

Adjusted costs �0.053 Intercept 0.8619 �0.046 Intercept 0.7208

Cycle time 0.8384 Cycle time 0.7042

Direct labor 0.9846 Lot size 0.0001 0.9677 Cycle time 0.0001


Cycle time2 0.0001

Indirect labor 0.9615 Lot size 0.0518 0.9472 Cycle time 0.0001


Cycle time2 0.0001

Benefits 0.9773 Lot size 0.0098 0.9632 Cycle time 0.0001


Cycle time2 0.0001

Supplies 0.9750 Lot size 0.0034 0.9577 Cycle time 0.0001


Cycle time2 0.0001

Repair & maint. 0.9771 Lot size 0.0001 0.9569 Cycle time 0.0001


Cycle time2 0.0001

Sundry 0.7800 Lot size 0.0001 0.7146 Cycle time 0.0009

Cycle time2 0.0503

Depreciation 0.8801 Cycle time 0.0001 0.8591 Cycle time 0.0001

Cycle time2 0.0039 Cycle time2 0.0001

Lease 0.4574 Cycle time 0.0018 0.4720 Cycle time 0.0014

Cycle time2 0.0108 Cycle time2 0.0088

Taxes 0.9360 Lot size 0.0001 0.9104 Cycle time 0.0001

Cycle time2 0.0053

Occupancy 0.9714 Lot size 0.0246 0.9619 Cycle time 0.0001


Cycle time2 0.0002

Utilities 0.9826 Lot size 0.0004 0.9695 Cycle time 0.0001


Cycle time2 0.0001

Lint free paper 0.9707 Lot size 0.0141 0.9634 Cycle time 0.0001


Cycle time2 0.0001

Services 0.7050 Lot size 0.1737 0.7023 Cycle time 0.0002


Cycle time2 0.1089


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Table 4

ANOVA test of simulation costs

Dependent

variable

Independent

variable

Prob4F

Production

costs

Overhead

costs

Prod 1 Costs Lot size 0.0089 0.0001




An ANOVA procedure is utilized to testHypothesis 2. Table 4 shows the results of thisanalysis of variance test. We concluded from theresults shown in Table 4 that, at the 0.05 level ofsignificance there were significant differences inproduction costs due to changes in lot size for eachof the three product types.

To test for changes in the overhead costs, thefollowing hypothesis is made:

Hypothesis 3.

Ho3: The overhead costs at the various lot sizesare all equal, versus the alternative hypothesis of,

Ha3: The overhead costs at the various lot sizesare not all equal.

Total operating expenses are calculated for onesimulated year. These operating expenses weredivided into two types of costs: direct and indirect.The direct costs are the production costs, specifi-cally the direct labor and consumable material costsof both setups and operations. The overhead costswere determined by subtracting the direct costsfrom the total operating expenses. Based upon theseoverhead costs, an ANOVA procedure was utilizedto test Hypothesis 3. Table 4 shows the results ofthis analysis of variance test. From the resultsshown in Table 4, we can again reject the nullhypothesis. There are significant differences inoverhead costs associated with changes in lot sizefor each of the three product types.

5. Analysis of results

Previous studies have suggested that lot sizedoes substantially impact the performance of the

job shop process flows, primarily due to theincreased number of setups required. Our researchshows how the interactions among the lot sizes ofmultiple products can affect not only a system’soutput and work-in-process inventory levels, butalso its cycle times, operating expenses, bottlenecklocations (see Table 5), and net profits. In additionto these findings, we are interested in determiningthe existence of a lower bound below which lot sizeshould not be set.

In the literature, many authors have shown, oreluded, that by reducing lot sizes, the firm’sproduction system(s) output and cycle time(s)would improve. The results of our researchsupport these assertions, and extend our knowl-edge that lower bounds on lot sizes do exist, belowwhich expected gains from lot size reduction willnot produce any further improvement in perfor-mance. Furthermore, our results demonstrate thatthere are significant interaction affects of lot sizesin the multiple product, multiple operation case.The exact determination of this lower bound isdependent upon the process design, the productmix, and the material release dates. Product mixand lot size are also shown to significantly affectproduct cycle times, operating expenses, andbottleneck location. Table 5 shows how lot sizesaffect the three products utilized in our simulation.

In Table 5 it can be seen that at all four materialrelease rates levels, using a standard lot size for allthree products, lot size reductions resulted inimprovements in both throughput and cycle times,except at the very small lot size of three units perlot (run 1). However, using mixed lot sizes gave thebest results in three of the four cases. At thematerial release rate of 96 units per shift, the mixedlot size run of 48, 3, and 48 (run 234) had the bestoverall average net revenues per wafer of through-put ($1210.62), while the standard lot size of 24units (run 254) had comparable average netrevenues per wafer of throughput ($1202.94). Asthe load upon the system increased, the effect oflot size upon the system is more pronounced asillustrated in runs 75, 82, and 119. As mentionedpreviously, the operating costs, and thus, the netrevenues are based upon known equipmentutilization costs and regression based predictedoverhead costs.

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STable 5

Summary of simulation results

Run Prod Lot

size

Release

rate per

shift

Net profit

per unit of

throughput

Op expense

per unit of

throughput

Annual

throughput

Ending

WIP

level

Cycle time

(yr)

Make time

(hr)

Bottleneck

location

(Work

center #)

1 1 3 142 $541.33 $958.67 33,585 113,781 0.5478 4802.0 2

2 3 142 $174.98 $1325.02 26,421 127,908 0.5967 5231.0 2

3 3 142 $490.80 $1009.20 36,060 115,641 0.6429 5636.0 2

Average $402.37 $1097.63 0.5958 5223.0

Total 96,066 357,330

38 1 12 138 $1144.65 $355.35 95,976 12,996 0.1007 882.6 43

2 12 138 $1077.88 $422.12 94,596 15,888 0.1225 1074.0 43

3 12 138 $1135.22 $364.78 95,712 14,208 0.1087 953.2 43

Average $1119.25 $380.75 0.1106 969.0

Total 286,284 43,092

42 1 12 138 $1159.30 $340.70 100,944 4632 0.0446 391.0 2

2 24 132 $1138.46 $361.54 96,864 6408 0.0659 577.8 2

3 12 138 $1152.46 $347.54 100,680 4680 0.0455 399.0 2

Average $1150.07 $349.93 0.0520 455.9

Total 298,488 15,720

75 1 48 168 $(78.90) $1578.90 20,112 206,016 1.2355 10830.0 40

2 48 168 $(2179.50) $3679.50 10,128 226,512 1.3895 12180.0 40

3 48 168 $994.25 $505.75 65,952 119,520 0.7042 6173.0 40

Average $(421.38) $1921.38 1.1097 9727.7

Total 96,192 552,048

82 1 6 189 $953.82 $546.18 91,704 95,898 0.5254 4606.0 19

2 6 189 $719.37 $780.63 82,848 114,546 0.6270 5496.0 19

3 6 189 $819.70 $680.30 82,722 114,324 0.6259 5487.0 19

Average $830.96 $669.04 0.5928 5196.3

Total 257,274 324,768

93 1 24 180 $1200.11 $299.89 101,256 66,240 0.3848 3373.0 19

2 12 186 $1111.64 $388.36 99,732 77,136 0.4311 3779.0 19

3 24 180 $1200.69 $299.31 92,136 83,712 0.4766 4178.0 19

Average $1170.81 $329.19 0.4308 3776.7

Total 293,124 227,088

119 1 24 180 $957.72 $542.28 77,664 111,576 0.6415 5623.0 40

2 24 180 $730.50 $769.50 64,056 138,864 0.8003 7015.0 40

3 24 180 $1052.06 $447.94 96,120 75,192 0.4329 3795.0 40

Average $913.43 $586.57 0.6249 5477.7

Total 237,840 325,632

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S195 1 48 144 $1233.02 $266.98 101,520 17,712 0.1483 1300.0 40

2 6 144 $1066.53 $433.47 102,744 12,156 0.1020 894.2 40

3 6 144 $1131.51 $368.49 104,682 6906 0.0624 546.9 40

Average $1143.68 $356.32 0.1042 913.7

Total 308,946 36,774

205 1 48 144 $497.97 $1,002.03 25,152 160,032 1.1192 9811.0 40

2 48 144 $(512.18) $2,012.18 14,736 181,632 1.2982 11380.0 40

3 48 144 $1088.96 $411.04 64,128 85,584 0.6034 5289.0 40

Average $358.25 $1,141.75 1.0069 8826.7

Total 104,016 427,248

210 1 12 144 $1119.67 $380.33 93,144 25,896 0.1867 1637.0 43

2 12 144 $1042.77 $457.23 91,188 30,960 0.2239 1963.0 43

3 12 144 $1106.91 $393.09 92,076 28,356 0.2039 1787.0 43

Average $1089.79 $410.21

Total 276,408 85,212 0.2048 1795.7

217 1 6 96 $1152.77 $347.23 70,152 2208 0.0310 272.1 2

2 6 96 $1091.86 $408.14 70,152 2826 0.0395 346.0 2

3 6 96 $1145.54 $354.46 70,164 2316 0.0331 290.2 2

Average $1130.06 $369.94 0.0345 302.8

Total 210,468 7350

234 1 48 96 $1312.86 $187.14 70,176 3840 0.0547 479.7 2

2 3 96 $1172.86 $327.14 70,224 3264 0.0463 406.3 2

3 48 96 $1146.13 $353.87 70,236 2082 0.0296 259.3 2

Average $1210.62 $289.38 0.0436 381.8

Total 210,636 9188

254 1 24 96 $1222.10 $277.90 70,152 2640 0.0372 326.1 2

2 24 96 $1173.33 $326.67 70,200 3120 0.0440 385.9 2

3 24 96 $1213.39 $286.61 70,200 2808 0.0389 341.0 2

Average $1202.94 $297.06 0.0400 351.0

Total 210,552 8568

261 1 3 96 $1139.84 $360.16 70,158 2664 0.0369 323.6 2

2 3 96 $1076.47 $423.53 70,152 3369 0.0470 411.7 2

3 3 96 $1132.11 $367.89 70,089 2865 0.0391 343.0 2

Average $1116.14 $383.86 0.0410 359.4

Total 210,399 8898

282 1 48 96 $1308.73 $191.27 70,080 4080 0.0576 504.5 2

2 6 96 $1092.26 $407.74 70,170 2694 0.0380 333.0 2

3 3 96 $1133.80 $366.20 70,224 2226 0.0311 273.0 2

Average $1178.26 $321.74 0.0422 370.2

Total 210,474 9000

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Other than the degree of shared resources, theprimary difference between the single product caseand the multiple product case is the interaction ofthe product lot sizes. As products contend forshared resources, the lot size of the variousproducts will affect the operational performanceof these resources. Due to fluctuations andstatistical variance that is found in all processes,the negative effects of a less than optimal lot sizewill repel through a system, magnifying theproblems of the system’s natural fluctuations andvariance. Note in Table 5, for runs 205, and 210,the reduction in the standard lot size from 48 unitsper lot to 12 units per lot resulted in significantimprovements in the system’s output and cycletimes. Now note in Table 5, run 195, the mixed lotsizes of 48, 6, and 6 units per lot for products 1, 2,and 3, respectively, resulted in not only higheroutput levels and lower cycle time, but alsoresulted in higher net profits.

As stated by Goldratt and Cox (1992) andGoldratt and Fox (1996), the goal of the firm is tomake a profit, both in the present and in the future.As shown in Table 5, the interaction of lot sizesbetween multiple products can have significantimpacts upon not only the firm’s ability to meet itscompetitive objectives, but also its ability to makea profit. By taking a profit orientation, the modelsdeveloped and presented in this paper provide thejob shop operations manager a tool for maximizingthe performance and net profits of his operation.

Depending upon the firm’s competitive strate-gies and objectives, the results of applying theknowledge presented here can make one or moreof the following contributions:

1.
maximize net profits while simultaneouslydecreasing work-in-process across one or moreproducts,
2.
maximize net profits while simultaneouslyincreasing throughput across one or moreproducts,
3.
maximize net profits while simultaneouslydecreasing cycle times across one or moreproducts, or
4.
contingent upon further research, maintain ormove the bottleneck for one or more productsto a desired operation.
In a typical job shop operation there is alreadywork in the production stream. Furthermore, it isnot usual for new jobs to be introduced into thisexisting process stream of work. The contributionfrom this study could be recognized as giving theoperations manager the ability to appropriatelysize the new job’s lots and determine the appro-priate material release schedule for the new job,given the lot sizes and material release schedules ofthe work currently in the system, such that one ormore of the above contributions will occur. Withthe modeling tools developed here, it is evenpossible to adjust the lot sizes on future workreleases for the existing products so as toaccommodate the new product.

Fig. 3 shows the effects of lot sizes on the meanoperating expense per unit of throughput, themean net profit per unit of throughput, and theaverage cycle time for each of the three productsused. In order to show cycle times in this figurethey are scaled up by a factor of 500. This figure isconstructed from data generated by the simulationmodel. It must be noted that the amount of a givenproduct in the system, with respect to the system’supper capacity limit for that product, will affectthe degree to which lot size/product interactionsaffect cycle times. The operating expense and netprofit values for the three products are in respectto the number of units of output by the productprocess as opposed to the total number of units inthe system.

The operating expense and net profit curves inFig. 3 show that for all three products the curvesare correlated to their respective cycle times. Theuni-modal nature of these curves is due to theselection of the lot sizes. Lot sizes that are not neareven multiples of the respective product’s bot-tlenecking-resource’s load capacity introduce amulti-modal behavior in these curves. In fact,operating expenses per unit of throughput areobserved to rise substantially when lot sizes are noteven multiples of the bottleneck’s load capacity.

6. Conclusions

Cycle time in the semiconductor industry is ofgreat concern and has undergone much evaluation

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Fig. 3. Net profits and operating expenses per wafer of throughput with respect to cycle time.


as well. Chen et al. (1988) note the importance ofcycle time reduction in the semiconductor indus-try. They state that the total cycle time for atypical circuit (VLSI) is about 4 months (i.e. 0.334years), considering all stages of production. Forcustomized circuits, the total lead-time imposed oncustomers must be at least as large as the totalcycle time. If a facility can decrease cycle time, amajor competitive advantage exists because theproduct can be delivered sooner. Furthermore,carrying inventory of standardized products isdangerous. Forecasts of market demand may behighly inaccurate due to the long manufacturingintervals. Also, product life cycles are short in the

semiconductor industry; thus, the risk of obsoles-cence becomes a factor. Finally, there exists anegative correlation between cycle time and yieldin wafer fabrication center (Chen et al., 1988).Thus, a shorter cycle time will result in increasedyields due to a smaller chance of particlecontamination (Atherton and Dayhoff, 1986).These same concerns are also valid for otherindustries.

The research presented in this paper demon-strates the type of cycle time and net profitimprovements that can be expected through lotsize reduction, as well as establishing the existenceof a lower bound on these improvements. The

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affect of lot sizing and the interaction of multipleproducts on throughput and work-in-processinventory levels have also been shown. With theselection of the best combination of lot sizes,system output can be increased, and both work-in-process and cycle time can be reduced. Further-more, with the selection of the optimal combina-tion of lot sizes, net profits can be maximized.With the wrong combination of lot sizes, especiallyat higher material release rates, the productionsystem can become clogged with work-in-processand throughput will be diminished.

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the impact of lot-sizing on net profits and cycle times in the n-job, m-machine job shop with both...

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