evaluating alternative capacity strategies in

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Int. J. Production Economics 105 (2007) 591–606

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Evaluating alternative capacity strategies in semiconductormanufacturing under uncertain demand and price scenarios

Yon-Chun Chou�, C.-T. Cheng, Feng-Cheng Yang, Yi-Yu Liang

Graduate Institute of Industrial Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, Taipei 106, Taiwan

Received 12 October 2004; accepted 3 May 2006

Available online 4 August 2006

Abstract

Because product demand is very volatile and machine and process technologies are advanced at a rapid pace, capacity

planning, and investment in the semiconductor industry is a challenging task. Many studies have addressed mid- and short-

term machine portfolio planning tasks of capacity planning. However, capacity planning should be considered in a

framework of strategy planning in order to address the whole problem. This paper describes a method of analysis for

adapting capacity strategy to changing business environment. The paper has three major parts. In the first part, empirical

data analysis of a case study company yields predictive formulas for production and capacity costs. The uncertainty of

demand is also calibrated using the geometric Brownian motion process. In the second part, experiments are designed to

simulate demand and profit scenarios for comparing two capacity strategies. In the third part, the resultant data of

simulation are analysed to gain insights to the relative performance of the two strategies in various scenarios. The analysis

method provides a framework for formulating capacity strategy and for integrating capacity planning with business

planning.

r 2006 Elsevier B.V. All rights reserved.

Keywords: Capacity strategy; Semiconductor manufacturing; Capacity planning and investment; Real options; Geometric Brownian

motion; Manufacturing cost

1. Introduction

Capacity planning and investment is a challen-ging task in the semiconductor manufacturingindustry. The industry supplies integrated circuitdevices to many end-product industries such ascomputer, communications, and electronics, whichhave dynamic market demands themselves. Due tothe bullwhip effect of the supply chain (Geary et al.,

front matter r 2006 Elsevier B.V. All rights reserved

e.2006.05.006

ng author. +886 2 3366 9501;

2 5856.

ss: [email protected] (Y.-C. Chou).

2006), the demand as faced by semiconductormanufacturers is very volatile and the industry isplagued with repeating cycles of over- and under-capacity. Furthermore, machine and process tech-nologies are advanced (and become obsolete) at arapid pace. The cycle time of one generation oftechnology is no more than 3 years, yet it takes atleast 9 months to incrementally add capacity to anexisting plant and at least a year to equip a bareclean room of the factory to produce the first wafer.Complicating the matter of capacity investment isthe capital cost of capacity. A modern semiconduc-tor wafer fabrication plant requires a capital

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ARTICLE IN PRESSY.-C. Chou et al. / Int. J. Production Economics 105 (2007) 591–606592

investment of 2–3 billion US dollars and equipmentdepreciation accounts for approximately 70% of thetotal production cost. Investing in one single factoryis a high financial risk for even the largestcompanies in the industry.

Volatile demand, risk of technology obsolescence,long lead time, and high investment cost contributeto making capacity investment an overwhelmingdecision-making task for which a satisfactoryplanning methodology has not been found. Fig. 1shows the historical data of aggregate capacity andwafer output of a major semiconductor manufac-turing enterprise over a period of 10 years. Theaggregate capacity increased by 10 times. Thegrowth rate was higher in earlier years, duringwhich times the trend was also largely predictable.However, in the later half of the period the growthrate stabilized and began to show significantoscillation. The reasons for stabilization can beattributed to market saturation and poor return oncapacity investment. The reason for oscillation isattributable to the volatile nature of demand in theindustry.

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Installed Capacity

Wafer Output

Fig. 1. Growth in capacity and output

Fig. 2. Trends of total assets a

Fig. 2 is the quarterly total assets and the returnon equity (ROE) of the company from 1994 to 2003.While the capacity continued to increase, the ROEhas a decreasing slope for the trend line. The ROEof the company is at a level no better than what canbe commonly found in many matured industries.This phenomenon is not unique to any particularcompany in the industry; there are actually manyworse performers (Liang and Chou, 2003). Figs. 1and 2 also illustrate a pattern of life cycle similar towhat is exhibited in the growth process of manyhigh-tech industries and corporations. At the initialstage of growth, product demand increases rapidlyand profit margins are high. Most companies arenaturally inclined to pursuing a strategy of aggres-sive expansion. However, as competition intensifiesor the market begins to saturate, profit margins willdecrease and the ROE will settle down to certainequilibriums. A conservative strategy of expansionwould increasingly be justifiable, especially when themarket is volatile. In fact, a higher level of volatilitymight call for a more conservative strategy. If theindustry enters the matured stage with slowed

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of a semiconductor manufacturer.

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Table 1

Capacity planning tasks and objectives

Objective Tasks

Short-term Order fulfillment Order rescheduling

Alternative routing

Mid-term Machine portfolio

optimization

Machine purchase

Machine

decommission

Long-term Supporting business planning in technology

development and product planning

Y.-C. Chou et al. / Int. J. Production Economics 105 (2007) 591–606 593

growth but the company strategy remains aggres-sive, aggressive expansion will put the company ingreat financial risk.

Capacity planning has received significant atten-tion in the literature and in practice. Because thelead time of capacity provisioning is long, capacityplanning tasks can be classified by their planninghorizon (Table 1). In the short-term, the overallcapacity is largely fixed, but with some room foradjustment through equipment set-up change-over(i.e., alternative routing). Therefore, capacity plan-ning problems are mainly about capacity allocationamong job orders and alternative routing planning.The granularity of capacity requirement analysis isat the machine and process step level. In themedium term, capacity can be changed by toolpurchase and decommission. It should be noted thatcapacity is expanded in small increments, bygradually populating the factory with more ma-chines. Capacity planning in this time frame ismainly a tool portfolio1 configuration problem. Thegranularity of planning is at the critical machine andmajor process stage level (Nazzal et al., 2006). In thelong term, the objective of capacity planning is toprepare for plant transition in anticipation of newprocess technology and new product and to supportstrategic plans of business.

A core issue of capacity planning is to configurethe tool portfolio. There is a combinatorial optimi-zation aspect to this problem. The computation oftool portfolio in semiconductor manufacturingsurpasses that of other manufacturing systems incomplexity. A wafer fabrication plant containshundreds of tools which are used to process tensor hundreds of product types (called process flows).

1Machines are called tools in this industry. The cost of a single

tool could be as high as 10 million US dollars. In this paper, the

words machine, tool and equipment are used interchangeably.

The manufacture of a product requires severalhundred steps in its process flow, with a tool visitedin each step. Most of the studies in the literatureaddress the problem of tool portfolio optimization.Swaminathan (2000) addressed the tool procure-ment decision over a planning horizon of multipletime periods. The uncertainty of product demand ismodelled by a set of demand scenarios. A largeinteger programme was used to minimize theexpected stock-out cost over all demand scenarios.Hood et al. (2003) followed the stochastic program-ming approach under demand uncertainty. The toolpurchase, wafer starts, and work assignment deci-sions are formulated as a large mixed-integerprogramme. Ahmed (2002) used multi-stage sto-chastic programming instead of two-stage stochasticprogramming to better model the flexibility of toolpurchase in later time periods bestowed by occur-rence of new events. The paper compares therelative merit between two-stage and multi-stagestochastic programming, and finds that the meritincreases with the number of stages and the numberof decision branches per stage. Christie and Wu(2002) used a stochastic programming formulationfor tool portfolio planning at the multiple-plantlevel.

A few papers addressed long-term and processissues related to capacity planning. The plant-sizingproblem is addressed by Benavides et al. (1999).Product demand is assumed to follow a geometricBrownian motion (GBM) process. The timingdecisions are modelled as an optimal stoppingproblem. The paper shows that optimal trade-offbetween economics of scale and flexibility can bereached by a sequential deployment of modularplants. Karabuk and Wu (2001) considered thecoordination problem between production managerand marketing management within one firm, that is,to blend the two forces that drive the decisions oncapacity planning. Two types of uncertainties aremodelled: one is capacity estimation and the other isdemand volatility. Stochastic programming is usedto solve the optimal capacity plan.

There are four models of tool portfolio andcapacity planning in the literature: (1) spreadsheetmodels, (2) multi-criteria search procedures, (3)mixed-integer mathematical programming models,and (4) stochastic programming models. Theobjective functions typically include terms ofrevenue, inventory cost, outsourcing cost, equip-ment cost, shortage cost, and machine utilization.Spreadsheet models are often used in practice


(Neudorff, 1999; Witte, 1996; Wu et al., 1998). Theyare used to compute utilization and throughout.Since flow time is also an important performancemeasure of tool portfolio, multi-criteria searchprocedures can also be used to find the optimaltool portfolio (Chou and Wu, 2002). Inthe literature, the most common models forcapacity planning are to use mixed-integer pro-gramming or stochastic programming to optimizetool portfolio decisions. Stochastic programming isa probabilistic optimization approach for manykinds of planning problems. The uncertainty isusually modelled by a finite number of scenarios.Due to different structures of the decision process,the stochastic programs are either formulated astwo-stage or multi-stage. Depending on applicationor focus, the decision variables range from machineto plant, and the scope may cover one or multipletime periods and one or multiple plants. In theliterature, the conventional logic of capacity plan-ning is to have sufficient capacity which willsatisfy product demands. The goal is typically tomaximize the profit, without considering the asso-ciated risk.

Two capacity strategies can be identified in theliterature: reactive and conservative. Liang andChou (2003) utilized the real-option theory indetermining capacity level. Capacity decisions aremade by taking into consideration the option ofwaiting for more demand information to materi-alize. This method amounts to a conservativestrategy. An alternative strategy is to reactivelyadjust the capacity plan according to changes indemand forecast. If the demand is volatile, orcapacity investment is irreversible, or the lead timeof capacity expansion is long, this strategy couldeasily lead to imbalance between the capacity anddemand.

The two strategies have their respective strength;their relative performance will depend on thecircumstance. In practice and in the literature, thereactive strategy is the dominant strategy. Eventhough demand is known to be uncertain, thecommon objective of capacity planning is still to‘‘satisfy’’ the demand. This inclination can be seenfrom the objective function of mathematical modelsfor tool portfolio planning. The objective functionsare primarily to maximize the revenue (or profit)subtracted by penalty for capacity shortage. Thisstrategy is a logical consequence of the corporatestructure of many enterprises. For example, in theso-called integrated design and manufacturing

companies, product plans and demand plans aredeveloped first. A capacity plan must support theirexecution. Consequently, the demand forecast thatis implicit in product and business plans will be usedas the input to capacity planning. Although theuncertainty must have been taken into considera-tion in business planning, the context is likely to belost in transferring the demand data to capacityplanning.

The four planning tasks identified in Table 1 havenot fully addressed the challenges posed by theuncertainties in demand, technology, and the returnon investment. In industries in which manufacturingcapacity is flexible and requires little capital invest-ment, business planning of product lines, marketing,and pricing does not have to be tightly integratedwith capacity planning. Capacity planning can bedone sequentially after business planning is com-pleted. However, if capacity investment requirementis large and investment is irreversible, capacityplanning must be integrated with business planning;otherwise, financial well-being would be subjectedto serious risk. Capacity investment in semiconduc-tor manufacturing is huge; it has a direct impact onthe subsistence of manufacturing capability. There-fore, the corporate business strategy must betranslated to, supported by, and integrated with itscapacity strategy. In addition, capacity strategymust be adjusted to the life cycle of product,enterprise, and even the industry. It is well knownthat products and processes usually have a life cycle.As revealed in Fig. 1, manufacturing enterprisesalso have a life cycle, although in a slightly differentway. In the initial stages of rapid growth, capacitystrategy should be more aggressive in order tosecure market share. As the market matured, thecapacity strategy should be more conservative inorder to avoid technology obsolescence. However, itremains to be determined what the trigger conditionis for a shift of strategy.

The focus of this paper is on the problem ofadapting capacity strategy according to the char-acteristics of demand and business plan. Thetreatment of the problem will complement the fourtasks of Table 1 in addressing the problem ofcapacity planning. The problem background—un-certainties, high investment cost, long lead time ofcapacity provisioning, etc.—are not unique to thesemiconductor industry. Other emerging high-techindustries, such as the liquid crystal displayindustry, also face similar challenges. The semicon-ductor industry has a mass production history of

ARTICLE IN PRESSY.-C. Chou et al. / Int. J. Production Economics 105 (2007) 591–606 595

approximately 30 years. It has gone through severaleconomic cycles and competition is fierce. Fig. 3shows the worldwide microchip sales over the last30 years in billions of dollars (the last data point isan estimate). The trend before 1995 appearedpredictable, but the industry seemed to enter anera of great volatility after 1995. Semiconductormanufacturing as a case study offers unparallelopportunities to study modern challenges of capa-city planning and investment.

In this paper, a framework of analysis and designof capacity strategies in an uncertain environmentof demand and technology is described. The frame-work is supported by empirical data analysis insemiconductor manufacturing. The remainder ofthis paper comprises of four parts. In Section 2,results of empirical data analysis for the character-istics of demand, production cost, and revenuetrend of semiconductor manufacturing are pre-sented. Then, scenario design for strategy analysisis described in Section 3. In Sections 4 and 5, twostrategies of capacity planning are analysed andcompared by using statistical methods. Finally,Section 6 concludes the discussions.

Fig. 3. Worldwide m

Fig. 4. The fixed cost per un

2. Data analysis

Capacity planning usually takes into considera-tion market share, revenue, profit, ROE, andindustry trend. In the first four subsections of thissection, the financial and capacity data of a casestudy company are first analysed in order toestimate the trends of the fixed assets cost, materialand labour costs (ML), operating expenses (OE),and average selling price (ASP). Then, in Section 2.5,worldwide demand of several market segments isanalysed to characterize the variability of productdemand. The analysis yields surprising results whichmake it possible to analyse different strategies ofcapacity. The data of the case study company coversa period of 10 years (from 1994 to 2003).

2.1. Capacity cost

The fixed cost of semiconductor manufacturing isprimarily incurred by investment in machines andequipment. It is largely irreversible and is reflectedin the fixed assets and accumulated depreciation inthe financial statement. Fig. 4 is the historical

icrochip sales.

it capacity per quarter.


capacity cost per capacity unit (200mm quarterlywafer equivalent). A trend of increasing cost couldbe easily observed. It also appears that a lineartrend line is a good approximation. Using the firstquarter of 1994 as the base period, Eq. (1) is theresultant regression equation for the fixed cost percapacity unit ðR2 ¼ 0:689Þ

FCðtÞ ¼ 6374:95þ 127:25t. (1)

The cost increases by approximately 2% perquarter (127.25/6374.95) at the base period. Con-sidering that prices are affected by many factors,this result that capacity cost can be reasonablypredicted with a linear trend line is quite surprising;some explanation of its possible cause is warranted.The technology content of processing equipment insemiconductor manufacturing is very high. Equip-ment providers must continue to invest heavily inresearch and development (R&D). As the technol-ogy is advanced, the cost of developing newmachines also increases. For each type of processingmachines, there are only a few providers world-wide—and mostly in the developed countries.Because the equipment market is an oligopoly withstrong competition, it is logical to expect that theprofit margin and cost of R&D would maintaintheir stable rate of increase. Therefore, the cost ofmanufacturing capacity is likely to also maintainsimilar appreciation.

2.2. Direct materials and labour costs

By definition in cost accounting, direct materialsand labour (M&L) costs are proportional toproduction output. Fig. 5 shows the average M&Lcosts per wafer that is manufactured. Similar tocapacity cost, the direct M&L costs can also bereasonably modelled by a linear trend. Eq. (2) is the

Fig. 5. The direct materials an

regression equation:

ML ¼ 406:28þ 3:37t ðper wafer outputÞ. (2)

The cost increases by approximately 0.83% perquarter at the base period. Direct materials, i.e., rawwafers and labour are mostly sourced locally.Comparing Eqs. (1) and (2), the slope and theincrease in percentage of the ML costs are muchsmaller than those of the capacity cost.

2.3. Operating expenses

OE include advertisement, marketing, and R&Dcosts. OE are proportional to the scale of opera-tions, which could be measured by the capacity levelor the output of production. The correlationcoefficient between the OE and capacity andbetween OE and output turns out to be 0.94 and0.88, respectively, indicating high level of correla-tion. Fig. 6 is a graph validating that it is moreaccurate to use capacity level than to use productionoutput to estimate the unit OE. A second support-ing argument can be gleaned from data in Fig. 1.The production output is immediately influenced bythe ups and downs of the economic cycles, but OEare more resilient to economic fluctuations. In fact,some components of OE, such as R&D expendituremight be immune to short-term fluctuations ofmarket demand. Thus, using the production outputas the denominator to compute the unit OE is morelikely to result in distortion.

Eq. (3) is the resultant regression equation forunit OE. It turns out that the average operatingexpense per unit of capacity could be reasonablytreated as a constant.

Operating expenses ¼ 131:44 ðper unit of capacityÞ.

(3)

d labour costs per wafer.

ARTICLE IN PRESS

Fig. 6. Operating expenses per unit of capacity and output.

Fig. 7. Average selling price and its trend.

2Computed by dividing the total revenue by the total output in

wafers.


Since one would normally expect that any cost toincrease at a rate that is at least equal to theinflation rate in the long term, rather than to stay ata constant, we will offer an explanation. It isplausible that the effect of inflation is cancelled outby the increase in the scale of production. (Note: Theaverage operating expense per wafer output doeshave a regression line of positive slope. However, theslope is mere $1.93 USD per quarter.)

Contrary to common belief, R&D cost is notsignificant as a percentage of the total cost. In Fig. 6,R&D expense is one of three components of the OE.The explanation is quite simple. Although R&Dcost is not insignificant in absolute term. It is paledby the cost of capacity. Note that one singlemachine could cost 10 million US dollars andR&D work is done on production equipment.

2.4. Average selling price

As shown in the previous three subsections, thefixed costs, direct M&L costs, and OE have very

predictable trends. By using Eqs. (1)–(3), the cost offuture capacity plans could be estimated withaccuracy. In comparison, the ASP manifests an-other phenomenon. Fig. 7 is the ASP2 of the casestudy company over the same 10-year duration. It israther surprising to observe that no significantprogress was made in the ASP, while the companyhas made significant progress in technologies andhas became an industry leader in her sphere ofbusiness. Semiconductor manufacturing companiesare compelled to continuously advance their processtechnologies. However, the ASP is under tremen-dous market pressure; it is not very easy to makeprogress in this aspect. This fact is in stark contrastto the increasing trend of capacity cost and it plays amajor role in exacerbating the need to adaptingcapacity strategy.

Two trends can be gleaned from data in Fig. 7.First, linear regression can be used to construct a


long-term trend line over the entire duration:

ASPðtÞ ¼ 1370þ 5:28t. (4)

Because the technology cycle time is 2–3 years onaverage but different companies’ progress might notbe in sync, a company might gain advantage intechnology temporarily. But, over the long run theadvantage might or might not be sustainable.Therefore, an alternative visualization of the ASPtrend is possible. In addition to Eq. (4), the ASPcould be alternatively modelled as a step function.The ASP remains flat over medium term. Forinstance, the ASP is approximately $1200 between1997 and 2000; it then increased to $1600 after 2000.Both long-term and step function trends arerelevant in capacity planning, as the life time ofequipment falls somewhere in between. In the nextsection, both scenarios are included in the analysisof strategy. Also, we will further justify flat ASP (inthe short run) by analysing the relative ASP ofmultiple companies.

2.5. Demand variation and modelling

That the variation of demand is very high in thesemiconductor industry is well known. However,how to measure the variability and incorporate thevariability factor in capacity planning remains to bestudied. GBM models have frequently been used tomodel the movement of stock prices, a best-knownexample of variability. The valuation formula forstock options that were derived by Black andScholes (1973) is based on the assumption ofGBM processes. Benavides et al. (1999) also useda GBM process to model the demand of semicon-ductor products. The formula of the GBM modeladopted in this paper is first summarized in the nextparagraph, followed by calibration of its parametersusing industry data.

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Fig. 8. The logarithmic growth

Let qt be the demand of time t. If qt follows aGBM process, then the change in demand can beexpressed by the equation dqt ¼ mqt dtþ sqt dwt,where dwt ¼ �t

ffiffiffiffiffidtp

, and et follows the standardnormal distribution. The m is called the driftparameter which can be ‘‘roughly’’ interpreted as ameasure of the long-term growth rate and s is thevolatility parameter. Let the base period be t0. Thelogarithm of the drift parameter rt will follow anormal distribution with mean ðm� s2=2Þt andvariance s2t (Tsay, 2002):

rt ¼ lnqt0þt

qt0

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rt�N½ðm� s2=2Þt;s2t�. (5)

In the Industry Economic Model (InternationalSEMATECH, 2002), the worldwide demands ofsemiconductor integrated circuits (IC) are classifiedby process type and technology level into severalcategories: leading edge memory, leading edge logic,other leading edge, other IC, and other semicon-ductor circuits. Historical data and forecasts for thedemands of the five market segments are attached inthe Appendix. It can be easily observed that thereis significant variation in demand. In order tocalibrate the variation, we first applied the Dickey–Fuller test to the five time series. At the significantlevel of 0.05, the p-value is far greater than 0.05 forall five time series, indicating that they are non-stationary. Next, the original time series areconverted to time series of logarithmic growth rt.The resultant time series are stationary (left figure ofFig. 8), with a p-value of 0.0011, 0.0018, 0.0006,o0.0001, and 0.0009, respectively. Furthermore, thelogarithmic growth has a bell-shaped histogram(right figure). The objective of this study is notabout developing a model for demand forecast.Instead, we are interested in finding a mathematicaltool that is reasonably accurate in calibrating the

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variability. Based on the empirical evidence ofFig. 8, we believe that the GBM process is areasonable choice.

3. Designing scenarios for strategy analysis

In order to integrate capacity planning withbusiness planning, we will first describe somespecificity of the industry and the industrial practicein order to define the problem. In this industry, the‘‘shell’’ and clean room of the factory is built firstand machines are installed gradually over time.Depending on the market condition, it usually takes2–3 years to build up a factory to its full capacity.Thus, capacity expansion is usually a ‘‘continuing’’and dynamic process of small increments (as shownin Fig. 1). This is quite different from capacityexpansion of most other industries, in whichexpansion projects have well-planned schedule andsize. We believe that this continuous naturewarrants some rethinking of investment analysiswhich is addressed in this section.

The semiconductor manufacturing industry isnormally associated with high technology. How-ever, it is rather ironic that companies withadvanced process technology are not guaranteedto be the winners. Over the last 10 years, manycompanies in this category chose to either exit fromthe industry or scale down production and tooutsource manufacturing to foundry manufac-turers. But, if technology is not the sole sufficientcondition of surviving, then what are the otherconditions? Because the volatility in demand andthe high cost of capacity create great financial risk,our hypothesis is that a sound strategy of capacityinvestment is one of them and good financialperformance is the other and these two factors areclosely related. Another characteristic of the in-dustry is that companies in the industry must havethe will and resources to stay in the industry for thelong haul in both technology development andcapacity investment. The entry and staying powerbarriers are high. Therefore, we argue that thenormal criteria of investment analysis are notsufficient. Before we continue, we will first definethe concept of perpetual manufacturing capability.

Definition (Perpetual manufacturing capability).Perpetual manufacturing capability is the capabilityof a company to continuously thrive in high-technology manufacturing for the long run. Thiscapability will include the ability to continuouslydevelop new manufacturing technologies and to

have sufficient financial resources to continuouslyinvest in modern manufacturing facility. Theemphasis of this definition is on perpetuality.Outsourcing management is excluded from manu-facturing capability.

We next stipulate the requirements on the returnson capacity investment for perpetual manufacturingcapability. Because technologies (including ma-chines and processes) are advanced in a rapid pacein the industry, all companies have little option butto continue investing in R&D and in new technol-ogy; technology laggards will quickly be forced tomake a decision to exit the industry. In mostindustries, investment decisions are justified bysome forms of ROI analysis. A project is deemedeconomically feasible, if its expected ROI exceeds acertain threshold level. Because of the perpetualnature, capacity investment in this industry shouldnot be evaluated by using the one-time ROI analysisalone; more stringent requirements need to bedevised.

Investment projects can normally be funded byraising capital, through debt or equity. However,the capacity cost in this industry has anotherescalating cost facet, beside an increasing trend.The industry is at the juncture of migrating fromolder 200mm-wafer to 300mm-wafter fabricationplants. A 200mm-wafer plant requires an invest-ment of $1 billion dollars while a 300mm waferplant requires $2–3 billion dollars. This creates aquantum hurdle for perpetual capability. (Somecompanies have tried to share the cost through jointventure. But this business model has not producedsuccess stories.)

Because of the perpetuality requirements, weargue that investment on capacity must generatesufficient net cash flow and show good performanceon returns. New investment must be at leastpartially funded by retained cash flow. Also, theexpected performance on accounting measures mustbe sound; otherwise, it would be very difficult toraise capital for the next generation of capacity,given the tremendous risk and poor track records ofthe industry.

Because capacity decision has a direct effect ontotal fixed assets and the depreciation of fixed assetsaccounts for a high percentage of the productioncost, we propose that operating income (OI) andreturn on fixed assets (ROFA) be used as theperformance measures for evaluating capacitystrategies. OI is computed by subtracting ML, OEand depreciation cost (DC) from revenue (R),


as shown in the following equation. By includingDC, the OI measure we used is therefore a modifiedmeasure of OI:

OIt ¼ Rt �MLt �OEt �DCt

¼ ASPtOt �MLt �OEt � FAt=l,

ROFAt ¼ OIt=FAt, (6)

where Ot is the production volume, FAt is the fixedassets, l is the life time, and t is the time index. OI isessentially the net cash flow with some minoradjustment to cash outflow due to equipmentpurchase. Because the unit cost of equipment couldbe very significant, cash outflow normally has highlevel of fluctuation. In Eq. (6), equipment expense isspread over the equipment life time. We chose to useROFA as the second performance measure, insteadof the more common ROE, in order to have a moredirect link between capacity decision and financialperformance.

The OI and ROFA measures are complimentary.OI can be regarded as a surrogate measure formarket share (since the majority of the costs aresunken), whereas ROFA is a surrogate measure forthe ROE. Having a large market share does notguarantee a higher ROFA. In fact, the contrarymight to be true in the problem setting that is underdiscussion here. We will use a numerical example toshow the computation of the threshold to demon-strate how the perpetuality requirement can betranslated into requirements on ROFA and OI.

Numerical Example: ROFA and OI.The equipment life time is 5 years on average by

the industry norm. We could postulate that if acompany owning a 200mm plant is to migrate to a300mm plant in 5 years, its equity must show anincrease commensurate with the increase in the

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Fig. 9. Relative ASP of co

factory cost. Otherwise, the company will not beable to survive in the industry. Therefore, to achievethe perpetual capability, and considering capacityexpansion is continuous, the ROFA should be atleast 2.0 in 5 years, or 3.53% per quarter:

ð1þROFAÞ20X2:0) ROFAX3:53%.

Assume a current initial capacity of one millionwafers per quarter (Fig. 1). That capacity will have aremnant value of zero after 5 years of depreciation.Based on the trend of capacity cost, the unit cost ofcapacity will be $14,000 in 5 years. Therefore, it canbe computed that a total of 14 billions of OI must beaccumulated over the 5 years in order to replenishthe capacity.

We will now describe the business scenarios inwhich competing capacity strategies are compared.The scenarios are defined by the variable factors ofdemand and profit. In this study, the GBM processhas been used to calibrate the uncertainty ofdemand. As the demand is beyond the control ofany single company, the drift and volatility para-meters are treated as endogenous variables. It hasbeen shown in previous section that the ASP can bemodelled as a linear function of time or as a stepfunction. Both models suggest that the ASP couldbe treated as constant during the life time ofequipment. Fig. 9 shows the recent ASP of majorcompetitors of the industry. This industry is anoligopoly with strong competition between firms.Microchips are used in numerous computer, com-munications, and consumer electronic products. Butthey account for a small part of the total cost of theend products. Pricing at the semiconductor manu-facturing stage usually does not have a large impacton the demand of end products in the long run.Therefore, price is usually not a management lever

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mpeting companies.


to influence demand. (An exception might be CPUproducts. But, CPU business is unique and is notwithin the scope of this paper.) Instead, thecompetitive factors are manufacturing technologyand engineering and manufacturing services (suchas design services, responsiveness, capacity plan,supply reliability, and order flexibility). The latterhas become more important in the supply chain ofsemiconductor manufacturing. As shown in Fig. 9,although there is significant difference in prices, therelative prices are remarkably stable over the years.Therefore, in our scenario design, we will treat bothdemand and price as exogenous and independentfactors. The difference in prices can be attributed togaps in both technology and services, which cannotbe closed in the short term. Therefore, pricing is notincluded as a decision variable in capacity require-ment analysis.

Based on the empirical data analysis of Section 2,nine demand scenarios of Table 2 are used in thestrategy analysis. The parameter m will be alterna-tively referred to as the demand growth rate, andthe parameter s as the demand volatility.

The profit scenario is further defined by fixed cost,M&L costs, OE, and ASP, by using Eqs. (1)–(4),

Table 2

Nine demand scenarios

s m

0.23 0.28 0.33

0.25 # 1 # 2 # 3

0.33 # 4 # 5 # 6

0.41 # 7 # 8 # 9

Table 3

Factors of profit scenarios

Factors FC

By capacity

Intercept 11,465

Slope 127

Factors ASP

Step improvement

Step 1 Step 2 Step 3

Intercept 1600 1800 2000

Slope 0 0 0

which are summarized in Table 3. More ASPscenarios have been added in order to include otherpossible improvements in ASP. Eq. (4) is a linearregression for the time series of ASP. The quarterlyrate of improvement is $5. However, more complexpatterns could be identified by a closer examinationof the time series. Because the scale of productionincreased by 10-folds in 10 years. The scale ofproduction in earlier years was quite small. Thecompany was a player in a niche market andenjoyed a higher profit margin. As the market sizegrew, the profit margin decreased. If the data before1997 are disregarded, the time series could bemodelled by a line or a step function of two levels.The linear line has a slope much greater than 5.0. Ifviewed as a step function, the ASP was kept at thelevel of $1200 for approximately 3 years and at$1600 for another 4 years. By hypothesizing allpossible courses of ASP improvement, three levelsof the step functions and three slopes of theregression line are included in Table 3. Based onTables 2 and 3, there are nine demand scenarios andsix profit scenarios. The total number of compoundscenarios is 54.

4. Computation procedures for capacity strategies

In this section, the computation procedures forthe reactive and conservative strategies are outlined.The GBM process is a continuous process. Toderive the numerical solution, the binomial latticeapproximation is frequently used in the literature(Luenberger, 1998). The approximation was firstproposed by Cox et al. (1979). Jarrow and Rudd(1983) improved the binomial lattice model. In this

ML OE

By output By capacity

537.71 131.44

3.37 0

Linear improvement

Growth 1 Growth 2 Growth 3

1581.2 1581.2 1581.2

5 10 15


paper, the Jarrow and Rudd model is adopted. Letthe demand at time t0 be qt0

, the demand in time

t0 þ Dt be qþt0þDt or q�t0þDt with equal probability of

0.5. Then qþt0þDt and q�t0þDt are given by

qþt0þDt ¼ qt0eu; u ¼ ðm� s2=2ÞDtþ sDt,

q�t0þDt ¼ qt0ev; v ¼ ðm� s2=2ÞDt� sDt,

where u and v are the up and down growth rates ofthe logarithm of demand, and m and s are theparameters of the underlying GRM process.

4.1. The reactive strategy

Let the current time be t, the capacity level be Ct,and the lead time of capacity deployment be d. Thecurrent decision is to determine the capacity level attime tþ d. Because capacity is irreversible, thecapacity decision is equivalent to determining thecapacity increment Dct. Eq. (5) is the stochasticmodel for the demand. Let qt be the demand at timet. The expected values of the drift parameter rt andthe demand qt are

r̄tþd ¼ ðm� s2=2Þd,

q̄tþd ¼ qter̄tþd .

The basic concept of the reactive strategy is tocompare the capacity level and expected demand. Ifthe expected demand of a future period ðq̄tþdÞ ishigher than the then existing capacity ðCtþd�1Þ, thenthe capacity is expanded. Therefore, the capacityincrement initiated in time t is

Dct ¼MAXð0; q̄tþd � Ctþd�1Þ

and the capacity trajectory is described byCtþ1 ¼ Ct þ Dct. This strategy represents a now-or-never decision for each time period ðtþ dÞ.Without considering all possible realizations offuture demands, it is also a myopic strategy.

4.2. The conservative strategy

When demands are uncertain, the value of a givencapacity depends on the demands that will berealized over the life time of the capacity. That partof capacity that exceeds the demand will notcontribute any revenue. The conservative strategyutilizes the real-option theory to evaluate the valueof capacity in the environment of uncertaindemand. The demand is represented by a binomiallattice model. Let the demand in scenario s of time t

be represented as qst and the probability that

scenario s will occur be pts. For notation brevity,

pts is simplified as ps with time t implicitly included in

s. By this notation, a state s is sometimes expressedas s(t) to make the time stage explicit. Under theconservative strategy, the capacity expansion deci-sion is made by considering all possible demandrealizations over the equipment life time. Let thecurrent time be t0. Given the binomial lattice modelof demand, the formulas of determining capacityincrement Dct0 have four major parts:

(1)
Compute the expected revenue for a given Dct0
over its life time. The effective capacity incre-ment (ECI) of Dct0 when evaluated against aparticular demand realization qs

t is defined asthat part of capacity increment that caneffectively generate revenue:

ECIðDct0 ;Ct�1; qstÞ ¼MIN½Dct0 ;maxðqs

t � Ct�1; 0Þ�.

The expected value of ECI with respect to allscenarios s of time period t is then

dt0;tðDct0 ;Ct�1; qstÞ ¼

Xs2S

psECIðDct0 ;Ct�1; qstÞ,

where the set S contains all demand states oftime t . The revenue that can be generated overthe life time [t0+d , t0+d+l] is

Rt0 ðDct0 ;ASP;PC; d; lÞ ¼Xt0þdþl

t¼t0þd

e�rðt�ðt0þdÞÞ

� ðASP� PCÞdt0 ;tðDct0 Þ,

where PC is the production cost and r is thediscount rate. The Rt0 ðDct0 Þ is also called thecurrent value of Dct0 .

(2)
Optimize the capacity increment based on netcash flow. From Eq. (1), the fixed cost of Dct isFCðtÞDct. Therefore, the optimal capacity in-crement at time t0 and a certain state s(t0) is
Dc�t0;sðt0Þ ¼ ArgmaxDct0

½Rt0 ðDct0Þ � FCðt0ÞDct0 �.

(7)

The corresponding net cash flow is

p�t0;sðt0Þ ¼ Rt0ðDc�t0 Þ � FCðt0ÞDc�t0;sðt0Þ.

(3)
Steps 1 and 2 are repeated for each node ðt; sÞ ofthe binomial lattice. In steps 1 and 2, the valueof waiting is not included in the optimization ofcapacity increment and its associated net cash


flow. Let F�t0;sðt0Þ be the total value of D�ct0 ,including the value of the waiting option. Then,

F�t0;sðt0Þ ¼ e�rEs½maxfp�t0þ1;s;F�t0þ1;sg�,

where the expectation E is taken over all statesin time t0+1.

(4)
When p�t0;sðt0Þ is greater than F�t0;sðt0Þ, the capacityis expanded at time t0, otherwise, the expansiondecision is postponed to time t0+1.
The industry practice is to use 4 years as the normallife time of process equipment and 1 additional yearto account for the salvage value. That is, the life timeis 5 years. In computing the total value of a capacityincrement, the value beyond its life time is zero andthe computation is performed backward. As thecapacity cost is spread evenly over the life time (incalculating OI), the remaining useful life of capacityat the end of analysis period is taken care of.

5. Performance analysis and comparison

The findings in Section 2 that production costsare predictable provide a good basis for inferringthe relative behaviour of capacity strategies in theuncertain environment of demand. In this section,the experimental results are summarized and dis-cussed. In each experiment (i.e., compound scenar-io), 10 demand paths are generated using MonteCarlo simulation. The two capacity strategies areapplied in order to simulate capacity expansiontrajectories. The performance measures ROFA andOI are then computed for each strategy. Theperformance of the reactive strategy is computedusing the demand paths. The performance of theconservative strategy is computed using a binomiallattice emanating from each node of the demandpaths. The step improvement and linear improve-ment scenarios of ASP are analysed separately.

5.1. The step improvement scenario of ASP

A step growth of ASP represents the scenario ofleaps in manufacturing technology. The regressionformulas that correlate performance measures withendogenous variables are shown in Eqs. (8)–(11).

Expected performance of the conservative strategy:

OI ðmillionsÞ ¼ � 10; 670� 243; 336m

þ 156:552mp� 10:368sp, ð8Þ

ROFA ð%Þ ¼ �7:39þ 0:00652p� 0:00074sp. (9)

Expected performance of the reactive strategy:

OI ðmillionsÞ ¼ � 3; 107� 163; 581m

þ 141:742mp� 165; 530ms, ð10Þ

ROFA ð%Þ ¼ �10:267þ 0:00850p� 0:00363sp.

(11)

If the regression analysis is applied to the difference ofperformance between the two strategies, the formulasare shown in Eqs. (12) and (13). The difference iscomputed by subtracting the OI and ROFA of theconservative strategy from those of the reactivestrategy.

DOI ðmillionsÞ ¼ �7491þ 28; 256s, (12)

DROFA ð%Þ ¼ 4:42mþ 5:04s� 0:00372mp. (13)

Insights can be gleaned from the formulas bycomparing corresponding coefficients. It should benoted that the magnitude of the prices is in thousands.Therefore, all terms of the above formulas are equallysignificant in magnitude; no terms should be deletedfor insignificance.

Insight (1): OI is affected by the combined effectof the growth rate and price (Eqs. (8) and (10)), notby the growth rate alone. In fact, if the trend ofprice is ignored in capacity planning, it is possiblethat a higher growth rate could lead to a lower OI.Take Eq. (8) as an example, if p is less than the ratioof 243336/156.552, OI will actually decrease with anincrease in m. This pitfall (that the growth indemand is necessarily beneficial) should be avoidedin capacity planning.

Insight (2): For either strategy, ROFA is notaffected by the growth rate (Eqs. (9) and (11)).Instead, it is determined by the price, subtracted bythe joint effect of demand volatility and price.

Insight (3): The detrimental effect of the demandvolatility is very significant. It is the deciding factorin choosing between the alternative capacity strate-gies (Eqs. (12) and (13) to some extent).

Insight (4): For the conservative strategy, OI isnegatively affected by the interaction between theprice and volatility parameter (�10.368). In con-trast, the reactive strategy is negatively affected bythe interaction between growth rate and volatilityparameter (�165530). The conservative strategy willnecessitate a closer attention to the price trend andthe reactive strategy will necessitate active monitor-ing of the demand volatility.

Insight (5): The volatility parameter has anegative effect on both performance measures. Its


effect is about 5 times more profound with thereactive strategy (0.00363–0.00074).

5.2. The linear growth scenario of ASP

A linear growth of ASP represents stable ad-vancement in manufacturing technology. The re-gression formulas are shown in Eqs. (14)–(19). Theparameter r represents the rate of increase of ASP indollars per quarter (Table 3)

�
Expected performance of the conservative strat-egy
OI ðmillionsÞ ¼ 8; 821� 8; 581s

þ 3; 281mr� 813sr, ð14Þ

ROFA ð%Þ ¼ 2:10þ 0:11212r. (15)

�
Expected performance of the reactive strategy
OI ðmillionsÞ ¼ 2; 173þ 59; 132m

þ 2; 235mr� 161; 521ms, ð16Þ

ROFA ð%Þ ¼ 2:92� 6:09sþ 0:12495r. (17)

�
Difference (the conservative strategy subtractedfrom the reactive strategy)
DOI ðmillionsÞ ¼ �25; 466mþ 103; 386ms, (18)

DROFA ð%Þ ¼ � 0:257� 1:57mþ 5:73s

� 0:04695mr. ð19Þ

Insight (6): It should be noted that, besides theslope of price improvement (r), the level of price hasan impact on OI and ROFA. The effect of theintercept of the prices is implicit in the constant

Fig. 10. The feasible region of scen

term of the above formulas. Taking this observationinto consideration, the two sets of formulas (8)–(13)and (14)–(19), have strikingly similar composition.Insights similar to those in Section 5.1 can bederived, including (1) OI is affected by the combinedeffect of demand growth and price, (2) ROFA is notaffected by the growth rate of demand, (3) thevolatility parameter is the crucial factor (withnegative coefficients in Eqs. (14)–(16)); (4) demandvolatility is more detrimental to the reactive strategythan to the conservative strategy (Eqs. (15) and (17))and the conservative strategy outperforms thereactive strategy when s is large (Eqs. (18) and (19)).

5.3. Adapting capacity strategy

Eqs. (8)–(19) provide useful information foradapting the capacity strategy in various scenariosof demand and ASP. Cross-over points could bedetermined by solving a set of linear inequalities asshown in Fig. 10. In the three-dimensional space ofm, s and ASP (level), the feasible region of scenariosthat satisfy the two perpetual capability conditionsis marked with the word ‘‘Positive’’: (1) ROFA43.53% and (2) OI414 Billions. For instance, if theconservative strategy is adopted and the ASP is onlymaintained at $1600, the objective of perpetualmanufacturing capability cannot be achieved.Fig. 10 provides a useful planning tool for adaptingcapacity strategy in the uncertain environment ofdemand, while taking into consideration the ASPtrend embedded in business plans.

6. Conclusions

Capacity planning and investment is a strategicissue in the semiconductor manufacturing industry.

arios for perpetual capability.

ARTICLE IN PRESS

0

5

10

15

20

25

30

35

40

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

LEM LEL OLE OIC OSC

Fig. 11. Worldwide demand of microchips by product segments.


In this paper, a new analysis method is presented foradapting capacity strategy in the environment ofuncertain demand and expected growth in ASP.This method is supported by empirical data analysisof the production and capacity costs of a majorsemiconductor manufacturer and by calibration ofthe uncertainty in demand in the industry. Manyinsights are gained in identifying the relativestrength of conservative and reactive capacitystrategies in various scenarios. There are severalimportant findings: (1) Growth in demand is notnecessarily beneficial in the uncertain industryenvironment. Volatility in demand is one of thecrucial factors in adapting capacity strategy. How-ever, it cannot be said that volatility alone is thedeciding factor. Capacity strategy should be chosenby considering the combined effect of demandgrowth and volatility. (2) The future trend of ASPis a more important factor than the growth indemand. (3) The corporate goals of increasingmarket share and increasing the return of equityare not necessarily coherent. In fact, we haveobserved in the industry that corporate goals doswitch between them. Since the two goals have adirect impact on the choice of capacity strategy, themethod described in this paper provides a frame-work for integrating capacity planning with busi-ness planning.

There are many other capital-intensive industries.See Luss (1982) for capacity expansion problems inheavy process industries, communication networkand public services (electric power, water resources,schools, etc.) The basic capacity expansion problemconsists of determining the sizes, timing, andlocations of the facilities. Semiconductor manufac-turing differs from those application areas in the

severity of demand volatility and the new require-ment of perpetual manufacturing capability. Thispaper identifies those differences, defines a new facetof perpetual capability, and develops a method forevaluating alternative capacity strategies.

Acknowledgement

This study was partially funded by NationalScience Council of Taiwan under contracts 92-2213-E-002-098 and 92-2213-E-002-027.

Appendix:. Worldwide demands of semiconductor

ICs

Data from 1991 to 2002 are historical data inmillions of wafers. Data after 2003 are forecastsmade by market research. All data are courtesy ofthe Industry Economic Model (Fig. 11).

References

Ahmed, S., 2002. Semiconductor tool planning via multi-stage

stochastic programming. In: Proceeding of the 2002 Interna-

tional Conference on Modeling and Analysis of Semiconduc-

tor Manufacturing, Tempe, Arizona, USA, pp. 153–157.

Benavides, D.L., Duley, J.R., Johnson, B.E., 1999. As good as it

gets: Optimal Fab design and deployment. IEEE Transactions

on Semiconductor Manufacturing 12 (3), 281–287.

Black, F., Scholes, M., 1973. The pricing of options and

corporate liabilities. The Journal of Political Economy 81

(3), 637–654.

Chou, Y.-C., Wu, C.-S., 2002. Economic analysis and optimiza-

tion of tool portfolio in semiconductor manufacturing. IEEE

Transactions on Semiconductor Manufacturing 15 (4),

447–453.


Christie, M.E.R., Wu, D., 2002. Semiconductor capacity plan-

ning: Stochastic modeling and computational studies. IIE

Transactions 34, 131–143.

Cox, J., Ross, S., Rubinstein, M., 1979. Option pricing: A simplified

approach. Journal of Financial Economics 7, 229–263.

Geary, S., Disney, S.M., Towill, D.R., 2006. On bullwhip in

supply chains—Historical review, present practice and ex-

pected future impact. International Journal of Production

Economics 101 (1), 2–18.

Hood, S.J., Bermon, S., Barahona, F., 2003. Capacity planning

under demand uncertainty for semiconductor manufacturing.

IEEE Transactions on Semiconductor Manufacturing 16 (2),

273–280.

International SEMATECH, 2002. Industry Economic Model.

Jarrow, A.R., Rudd, A., 1983. Option pricing (Irwin).

Karabuk, S., Wu, S.D., 2001. Coordinating strategic capacity

planning in the semiconductor industry. Technical Report

99T-11, Department of IMSE, Lehigh University.

Liang, Y.-Y., Chou, Y.-C., 2003. Option-based capacity planning

for semiconductor manufacturing. In: IEEE International

Symposium on Semiconductor Manufacturing, San Jose,

California, USA, September 30–October 2, pp. 77–80.

Luenberger, D.G., 1998. Investment Science. Oxford University

Press, Oxford (Chapter 11).

Luss, H., 1982. Operations research and capacity expansion

problems: A review. Operations Research 30 (5), 907–947.

Nazzal, D., Mollaghasemi, M., Anderson, D., 2006. A simula-

tion-based evaluation of the cost of cycle time reduction in

Agere Systems wafer fabrication facility—A case study.

International Journal of Production Economics 100 (1),

300–313.

Neudorff, J., 1999. Static capacity analysis using Microsoft

Visual Basic. In: International Conference on Semiconductor

Manufacturing Operational Modeling and Simulation,

San Francisco, pp. 207–212.

Swaminathan, J.M., 2000. Tool capacity planning for semicon-

ductor fabrication facilities under demand uncertainty.

European Journal of Operations Research 120, 545–558.

Tsay, R.S., 2002. Analysis of Financial Time Series. Wiley,

New York.

Witte, J.D., 1996. Using static capacity modelling techniques in

semiconductor manufacturing. In: IEEE/SEMI Advanced

Semiconductor Manufacturing Conference and Workshop,

pp. 31–35.

Wu, W.-F., Yang, J.-L., Liao, J.-T., 1998. Static capacity

checking system with cycle time considered. In: The Seventh

International Symposium on Semiconductor Manufacturing,

pp. 307–310.

evaluating alternative capacity strategies in

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