A DEA window analysis on the product family mix selection for
a semiconductor fabricator
Shu-Hsing Chung
a, Amy Hsin-I Lee
b,*, He-Yau Kang
c, Chih-Wei Lai
aaDepartment of Industrial Engineering and Management, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan bDepartment of Industrial Engineering and System Management, Chung Hua University, No. 707, Sec. 2, WuFu Road, Hsinchu 300, Taiwan
c
Department of Industrial Engineering and Management, National Chin-Yi University of Technology, 35, Lane 215, Sec. 1, Chung San Road, Taiping, Taichung 411, Taiwan
Abstract
In a competitive market, semiconductor fabricator must face an environment with multi-product types, multi-priority orders and demand changes in time. Since semiconductor fabrication has a very complicated production process, the above-stated characteristics make the production planning even more difficult. This paper applies data envelopment analysis (DEA) to find a set of product family mix that is efficient for the company to produce. To ensure long-term effectiveness in productivity and in profit gaining, window analysis is adopted to seek the most recommended set of product family mixes for manufacturing by measuring the performance changes over time. With this method, the performance of a mix in one period is compared not only with the performance of other mixes but also with its own performance in other periods. The proposed mechanism can provide guidance to the fabricator regarding strategies for aggregate planning so as to improve manufacturing efficiency.
2007 Elsevier Ltd. All rights reserved.
Keywords: Data envelopment analysis; DEA; Product family mix; Window analysis
1. Introduction
Today’s semiconductor market is not as prosperous as it was before, and the market has changed from producer-ori-ented to customer-oriproducer-ori-ented. A single optimization goal, such as throughput maximization or profit maximization that was usually pursued by companies, is not enough today to meet the production performance demanded by custom-ers. Performances such as on-time delivery and production cycle time are highly emphasized by customers. Therefore, companies need to consider both customer satisfaction in demand and the ultimate profit goal of companies.
As the economy fluctuates and product (or process) devel-ops, customer demands in product type and quantity change as a result. This also makes the demand of product family mix, where the products with similar processes are belonging
to the same product family, changes over time. Bottleneck utilization rate thus fluctuates, and this further has an impact on performance indicators such as production cycle time, delivery rate and work in process (WIP). The production performance evaluation in this kind of variant environment is much more important and difficult than the one in an envi-ronment with stable product types and quantities.
Previous researches usually focused on product mix determination; instead, this paper will select the most appropriate product family mix due to two primary rea-sons. First, the demand forecast of each product type is very difficult; on the other hand, the demand forecast of each product family, which consists of similar products, is relatively easier and more efficient for performance eval-uation. The second reason is that products belonging to the same product family have similar manufacturing processes, have certain degree of substitutability and require similar critical workstations such as bottleneck and capacity con-strained resource (CCR). On the other hand, different 0957-4174/$ - see front matter 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2007.07.011
*
Corresponding author. Tel.: +886 3 518 6582; fax: +886 3 518 6575. E-mail address:amylee@chu.edu.tw(Amy H.I. Lee).
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Expert Systems with Applications 35 (2008) 379–388
Expert Systems with Applications
product families require a more differentiated capacity demand. Therefore, the input and output indicators of dif-ferent product family mixes have a greater difference than the ones of different product mixes. As a result, the evalu-ation of alternatives on product family mixes will be more outstanding.
Product family mix determination is one of the core problems in current semiconductor production planning system. In wafer manufacturing, production processes such as photolithography, developing and etching have a unique characteristic of re-entry. The number of re-entry of a dis-tinct machine for each product family is different; there-fore, there often is a situation that different product families are required to be processed on the same machine at the same time. The situation can happen too even in the same product families for processing the re-entry opera-tions. Because of the above-mentioned process characteris-tic, a CCR may be overly utilized when customer orders are concentrated on a specific type of products, and this may lead to bottleneck wondering, decrease in throughput, elongation in production cycle time and decrease in deliv-ery rate. Product family mix not only has an impact on production performance, it also has an effect on a firm’s profit. This is because different product families have differ-ent process designs and recipes, and thus, prices. With dif-ferent product family mixes, profit obtained by the firm is different.
In solving the long-term product family mix problem, we should not only optimize one single performance factor, but rather we need to make sure that the performances on a number of indicators are satisfactory in order to maintain the competitive advantage of the fab. To consider numer-ous aspects of performance, in recent years, researches have been done to solve the product mix problem by adopting multiple criteria decision-making concept and related tools. However, scholars only focused on the deter-mination of product mix in a single period and did not
consider the performance problem in a long-term
demand-varying environment. In an environment with cus-tomer needs in unstable product mix and big demand fluctuation, the product family mix solved in a high demand time period may not be favorable in a low demand time period. Therefore, it is necessary to know how to set product family mix in a long term.
In this paper, multiple input and output indicators, such as total throughput, delivery rate, production cycle time, of the production system are included. In addition, the demand variation among several production periods are considered to find one or several product family mix alternatives that are most suitable for production. Using multiple performance indicators to evaluate system perfor-mance, previous methods usually required decision makers to give the importance weighting to each indicator, and the difference in weights given by different decision makers might make the performance evaluation results different. To prevent the weights from being influenced by the subjec-tivity of decision makers, data envelopment analysis
(DEA), a methodology that does not require pre-assign-ment of weights, is adopted here to evaluate product family mix. However, DEA alone cannot solve the problem of long-term product family mix performance evaluation. Therefore, window analysis that can compare the relative efficiency of product family mixes in different time periods is also applied in this paper. With the consideration of long-term demand fluctuation, one or a few product family mix alternatives that have long-term competitive advantage can be determined, and the firm can follow the recommen-dation in accepting orders to be competitive in the demand-varying environment.
The rest of this paper is organized as follows. Section 2
begins with a brief review of the product mix and priority
level problem in semiconductor manufacturing. Section 3
briefly reviews DEA methodology and window analysis.
Section 4 presents the product family mix evaluation
model. Some conclusions are made in Section5.
2. Product mix problem
Wafer fabs require a very high capital investment in plant and equipment, from $US 500 million to 1 billion each, and involve the most complex manufacturing system among all the manufacturing industries. Wafer fabrication has an important property, wafer process reentry, which refers to multiple visits by a wafer lot to the same processing center at different times. With 300–500 processing steps in a wafer process and a flow time of usually more than twenty days, the fabrication process is of high complexity. Product mix also has a very big impact to the production performance. Production performance in a wafer fab is a result of the interaction among product mix, equipment, inventory, pro-cess technology and scheduling practices. These factors change continuously if, for example, an unexpected equip-ment down time or a change in product mix happens fre-quently. The interaction between various complex factors makes production planning a very challenging task.
In order to be competitive and to satisfy customers’ demand of accelerating the speed of products entering into the market, a wafer fab often have multiple priority levels of orders, and higher priority must be given to some urgent lots. The production priorities can be divided into three categories: hot, rush and normal. A higher priority order can use a machine whenever there is no other higher prior-ity or equal priorprior-ity order in presence, but a lower priorprior-ity order has to wait till the machine becomes available. Because of a longer waiting time, lower priority orders result in a longer production cycle time. When there are too many lots with higher priority, the variation in shop floor performance will increase and the system throughput
will reduce (Atherton & Atherton, 1995; Ehteshami,
Petra-kian, & Shabe, 1992; Fronckowiak, Peikert, &
Nishino-hara, 1996; Narahari & Khan, 1997). A higher priority
order can result in the loss of machine capacity if a full loading policy is not required for batch machines and thus, machines are not fully utilized. Bottleneck shifting can
occur in consequence, and again have impact on the
pro-duction of lower priority orders. Narahari and Khan
(1997) developed an analytical method based on mean
value analysis (MVA) to predict the performance of semi-conductor manufacturing system in the presence of hot lots. The results also show that hot lots have a significant effect on the mean cycle time, variance of cycle time and throughput rate of normal lots. Because the changes in the ratios of different priority orders have a great impact on the system performance, fabs usually set a maximum limit on higher priority orders or fix the ratios for different
priority orders in advance.Chung, Pearn, and Lee (2006)
presented a preliminary application DEA to find a set of product mix efficient for the semiconductor manufacturing
company to achieve the optimal production.Kang and Lee
(2007) constructed a fuzzy analytic hierarchy process
(FAHP) method with entropy weight to generate perfor-mance ranking of different priority mixes in semiconductor manufacturing.
In summary, product family mix has a tremendous impact to the production system even when the priority mix is fixed, and many performance measures such as cycle time, WIP level, throughput, bottleneck utilization rate will be affected. Organizing the available data is a complicated task; however, DEA can provide a good method to deal with multiple inputs and outputs and to evaluate which product family mix can provide a more stabilized production envi-ronment and a better overall outcome for a wafer fab. 3. DEA methodology and window analysis
This paper proposed a data envelopment analysis (DEA) approach to solve the product family mix problem. The theory, development and applications of DEA, as well as its strengths and weaknesses, have been discussed in many papers, and therefore, only a brief review is presented
here (Charnes, Cooper, Lewin, & Seiford, 1994a; Cooper,
Seiford, & Tone, 2000). In 1957, Farrell first proposed
pro-duction frontier to measure propro-duction efficiency based on the concept of Pareto optimality, and a frontier function called the efficient production function is used to fit the
points as a piecewise linear function (Farrell, 1957). The
frontier is a reference for comparing the efficiency of vari-ous points, and production efficiency is separated into two types: technical efficiency and allocative efficiency. How-ever, the study was limited to single input and output.
Charnes, Cooper, and Rhodes (1978)extended Farrell’s
idea of linking the estimation of technical efficiency and production frontiers and developed DEA to generate com-prehensive performance measurement index. DEA is applied to measure efficiencies of decision-making units (DMU), whose efficiencies can be obtained through the evaluation of multiple inputs and outputs without the pre-assignment of the criteria weights. The position of a DMU relative to the efficient frontier, the envelopment constituted by all the DMUs, is measured as efficiency
(Charnes et al., 1994a). From the output perspective, if
the amount of an output can be increased for a DMU while the amount of any output does not decrease and the amount of all its inputs does not increase, then the DMU is inefficient. From the input perspective, if the amount of an input can be reduced while the amount of any other input does not increase and the amount of all its outputs does not decrease, then the DMU is inefficient. A DMU is found to be efficient if it lies on the efficient frontier, where there is no inefficiency in the utilization of inputs
and outputs (Charnes et al., 1994a).
DEA was first applied to investigate not-for-profit orga-nizations; however, in the past few years, more and more researches have extended the DEA methodology to an application in various sectors and domains to solve
multi-criteria optimization problems (Cooper et al., 2000). Since
its first introduction, an enormous number of DEA evolved models have been constructed to meet the different condi-tions of the problems for the past two decades, and DEA has been proved to be a promising technique for evaluating
performance (Charnes et al., 1994a; Cooper et al., 2000).
CCR model, the model we are adopting in this paper, is
introduced byCharnes et al. (1978)to generate efficiency in
ratio form, by obtaining directly from the data without requiring a priori specification of weights nor assuming functional forms of relations between inputs and outputs. An inefficient DMU can be made efficient by projection onto a point on the efficient frontier. The particular point of projection selected depends upon the orientation employed. In an output orientation (output maximization), maximal movement via proportional augmentation of out-puts is stressed. In other words, given the level of inout-puts used, what level of outputs can be best achieved. On the other hand, an input orientation (input minimization), maximal movement toward the frontier through propor-tional reduction of inputs is focused. That is, given the level of outputs produced, how much inputs can be reduced while maintaining their current level of outputs.
Below is a brief introduction of the input-oriented DEA
model developed by Charnes, Cooper and Rhodes, CCRd-I
(Charnes et al., 1978). Assume that there are n DMUs, and
each is represented by DMUjwhere j = 1, . . . k . . ., n. For
each DMU, there are m inputs (Xij; i = 1, . . ., m) and r
out-puts (Yrj; r = 1, . . ., s). The input of factor i for DMU j is
Xij, and the output of factor i for DMU j is Yrj. The
effi-ciency of DMUkcan be obtained as follows:
Min hk¼ hk e Xm i¼1 si þX s r¼1 sþr ! ð1Þ s:t X n j¼1 kjXij hkXikþ si ¼ 0; i ¼ 1; . . . ; m Xn j¼1 kjYrj sþr ¼ Yrk; r¼ 1; . . . ; s kj; si; s þ r P0; j¼ 1; . . . ; n; i ¼ 1; . . . ; m; r ¼ 1; . . . ; s ð2Þ
where s
i; sþr are the slack variables of inputs and outputs,
respectively, kjis the weight for DMUj, and hkis the
rela-tively efficiency indicator of the kth DMU.
A very small positive value e, which is called a
non-Archimedean small number, represents that all s
i and
sþr must be considered, and it is usually set to 104 or
106 in real application. When a DMU
k is relatively
effi-cient, its hk is one, and its s
i ¼ sþr ¼ 0. This implies that
the DMU is on the efficient frontier. If a DMU is relatively inefficient, its inputs and outputs deviated from the optimal
solution can be expressed as Xik¼ hkXik S
i and
Yrk¼ Yrkþ Sþr , respectively, where Xik and Yrk are the
inefficient input and output; Xik and Yrk are the input
and output for the DMU being efficient; and Si and Sþr
represent the required reduction and addition of input and output.
In the original DEA analysis, each DMU is observed only once, that is, each example is a cross-sectional analysis
of data (Charnes et al., 1994a). In many actual studies,
observations for DMUs are frequently available over mul-tiple time periods, and it is often important to perform a panel data analysis to focus on changes in efficiency over time. In such a circumstance, DEA window analysis can
be adopted to detect trend of a DMU over time (Asmild,
Paradi, Aggarwall, & Schaffnit, 2004; Charnes, Cooper,
& Seiford, 1994b; Yue, 1992). The underlying assumption
of window analysis, proposed byCharnes, Clark, Cooper,
and Golany (1985), is that of a moving-average analysis
and that each DMU’s efficiency is represented in the win-dow several times, instead of being represented by a single
summary score (Charnes et al., 1985; Charnes et al., 1994a,
1994b; Yue, 1992). Each DMU in a different period is
trea-ted as a different DMU, and the performance of a DMU in a period can be contrasted with its own performance in other periods as well as to the performance of other DMUs
(Asmild et al., 2004). In doing so, the number of data
points in the analysis is increased, and this can be usable when small sample sizes are under consideration.
The use of window analysis offers an opportunity to know how performance evolves through a sequence of overlapping windows. A brief window analysis review
is presented here (Sun, 1988). Assume there are N
alterna-tives, l = 1, . . ., N, and each alternative has data for period 1 to M, that is, m = 1, . . ., M. The window length is fixed to be K, and the data from period 1, 2, . . ., K will form the first window row, and the data from period 2, 3, . . ., K, K + 1 will form the second row, and so on. With the addition of one window, one more period on the right
will need to be shifted to, and a total of M K + 1 window
rows are existed. Each window is represented by
i = 1, . . ., M K + 1, and the ith window will consist of
the data in periods j = i, . . ., i + K 1. In the same
win-dow, there are K sets of data to be evaluated; therefore,
there are a total of N· K DMUs in that window.
DEA and window analysis have been adopted in many
researches. For example, Mahadevan (2002) adopted
them to explain the productivity growth performance of
Malaysia’s manufacturing sector using a panel data of 28
industries for 15 years. Asmild et al. (2004) combined
DEA window analysis with the Malmquist index approach in a study of the Canadian banking industry for 20 years. In order to evaluate the performance of product/family mixes over time, DEA window analysis will be used in this
paper.Charnes et al. (1994a)found that K = 3 or 4 tended
to yield the best balance of informativeness and stability of the efficiency scores, and the K = 4 quarter window facili-tated yearly planning and helped detect seasonal effects.
To apply window analysis, DEA is used first to evaluate the performance of all DMUs in the same window, and the
efficiency, El
i;j, of each DMU will be entered in the right
window position in the table. The procedure will be
repeated M K + 1 times to obtain all the efficiency values
in all windows. Then, window analysis used all the effi-ciency values of an alternative to generate some statistics
following Sueyoshi (1992) approaches. The average
effi-ciency (Ml) of alternative l is obtained by:
Ml¼ PMKþ1 i¼1 PiþK1 j¼i Ei;jl K ðM K þ 1Þ ; l¼ 1 . . . N ð3Þ
The variance among efficiencies of alternative l, Vl, is
calcu-lated by: Vl¼ PMKþ1 i PiþK1 j ðE l i;j MlÞ 2 K ðM K þ 1Þ 1 ; l¼ 1 . . . N ð4Þ
The variance of efficiency reflects the fluctuation of effi-ciency values for each alternative. If an alternative has higher average efficiency and small variance, its ranking can be higher compared to other alternatives.
Column range, CRl,m, can be used to compare the
fluc-tuations of efficiencies among the alternatives. In each alternative, because the data of the first period (m = 1) and last period (m = M) are being analyzed in only the first
and the M K + 1 window, respectively and thus, only
one efficiency value is obtained for each of the two win-dows, the efficiencies in the first and last periods will not be included in the calculation of CR values. For other peri-ods, the data of each alternative is used at least twice and at least two efficiency values are available for calculating CR
values. CRl,mis the difference between the largest and the
smallest efficiencies for alternative l in period m. That is, CRl;m ¼ MaxðEli;mÞ MinðE
l i;mÞ;
for i¼ maxðm K þ 1; 1Þ; . . . ; minðm; M K þ 1Þ
m¼ 1 . . . M
ð5Þ
CRl,mcan be used to evaluate the stability of efficiency of
an alternative in each period. Then, CRlis the overall
col-umn range for alternative l, and it shows the greatest vari-ation in efficiency of an alternative over different periods:
CRl¼ Maxm¼2; ...; M1ðCRl;mÞ ð6Þ
In addition, to understand the stability of an alternative over different periods, total range can be used. Total range is the difference between the maximum and minimum
efficiency values of an alternative in all windows. The total range for alternative l is:
TRl¼ MaxðEli;jÞ MinðE l
i;jÞ; for
i¼ 1; . . . ; M K þ 1; j¼ i; . . . ; i þ K 1 ð7Þ
For CRl,m, CRl, TRl, the smaller the value, the more
stabi-lized are the efficiency values for adopting alternative. With six evaluation periods and a window length of three peri-ods, the efficiency values and relevant evaluations are as
shown inTable 1.
4. Product family mix evaluation model 4.1. The selection of DEA model
To evaluate the long-term performance of product fam-ily mix in a wafer fab, we adopt the DEA window analysis in this paper for two reasons. One, window analysis can effectively analyze the relative performance of product fam-ily mixes in multiple periods and the variation of perfor-mances among the periods. Two, more input and output factors can be included in window analysis. In DEA, if the total number of input and output factors are greater than half of the number of DMUs, the correlation between the values of the original performance factors and the val-ues obtained through the DEA models becomes smaller,
and this makes the discriminating power decrease (Golany
& Roll, 1989). However, window analysis treats the
perfor-mance values of the same alternative in different periods as different DMUs. The number of DMUs, as a result, increases, and this can remedy the defect of the mathemat-ical model in DEA.
In window analysis, the DMUs in each window need a DEA mathematical model to calculate the efficient values, and the selection of a DEA model that is suitable for the environment stated in this paper is very important. As
sta-ted in Section3, CCR-I is applied to compare the input
effi-ciency of product family mixes based on the same level of output.
4.2. The selection of input and output factors
The selection of factors is essential. Factors should be selected properly to represent other correlated factors so
as to reduce number of inputs and outputs for the DEA model. For evaluating the product family mix in a semicon-ductor fab, data corresponding to these factors must meet the isotonicity required by DEA in order to obtain acute evaluation results. Isotonicity means that when an input increases, an output should not decrease, and vice versa
(Golany & Roll, 1989). If one factor has a negative or very
weak correlation with other inputs or outputs, in order to satisfy isotonicity, the factor needs to be deleted from the model. On the other hand, when two factors are perfectly positive correlated, that is, the correlation coefficient is one, the changes of one factor can be reflected by the changes of the other factor completely. In this case, only one factor is needed to evaluate the system performance.
Based on the above requirements, the most suitable input and output factors can be selected by the following steps:
Step 1: Have an interview with the relevant personnel and managers in the industry and obtain input and output factors that are considered to be most important. These factors are the candidate factors. Step 2: Construct a virtual wafer fab by building a simu-lation model. Run this model under different sce-narios so as to collect the data of the candidate factors.
Step 3: Calculate the correlation coefficients among the candidate factors. If there is any factor that has a negative correlation with other factors, delete the factor.
Step 4: If there are any two or more factors that are per-fectly positive correlated, select the factor that has higher correlations with the rest of the factors.
4.3. Input and output candidate factors
Financial performance is always the highest concern of the top management. Production performance, on the other hand, is impacted by product family mix. Therefore, these two aspects of performance should both be consid-ered in the evaluation of product family mix selection. After an interview with the related personnel of several semiconductor fabricators in Science-based Industrial Park in Taiwan, some candidate factors for wafer fab
Table 1
Window analysis of alternative l
Alternative Period 1 2 3 4 5 6 Mean efficiency Variance Total range
window l W1 El1;1 El1;2 El1;3 Ml Vl TRl W2 El2;2 El2;3 El2;4 W3 El3;3 El3;4 El3;5 W4 El4;4 El4;5 El4;6 CRl,m X CRl,2 CRl,3 CRl,4 CRl,5 X CRl X: omitted.
efficiency evaluation are selected. Below are the definitions of these factors:
1. WIP in front of photolithography workstation The circuit pattern of a wafer is constructed during photolithogra-phy. In order to achieve the pre-determined functions of final products, wafer batches must repeat photoli-thography activities, and thus, the re-entry characteris-tic is resulted. As WIP in front of the workstation increases, the smoothness of the wafer batch flow will be impacted. Therefore, this factor is an input that we would like to minimize from the view point of pro-duction control.
2. Bottleneck utilization rate The average utilization rate of the bottleneck in the system for a period of time. Because the number of layers and processing time are different for different product families, an inappropriate product family mix may result in the increase of bottle-neck utilization rate and production cycle time and may decrease delivery performance in consequence. There-fore, bottleneck utilization rate is categorized as an input for production control.
3. Number of CCR workstation If the utilization rate of a workstation is over 70% in a planning period, the work-station is treated as a capacity constraint resource (CCR). The more CCR workstations there are in a sys-tem, the higher is the probability of bottleneck shifting and the more unstable is the production process. Throughput may be decreased and delivery date may be delayed as a result. Thus, this factor is an input for production control.
4. Layer cycle time Layer cycle time measures the duration of time consumed by one photolithography activity and all the steps between the two consecutive photolithogra-phy activities. Time constraint characteristic must be considered for processing operations of each layer. For example, furnace activity must be processed in a limited time after the completion of wet etch process; otherwise, this batch of wafers must go through the wet etch pro-cess again. As layer cycle time increases, the probability of re-work increases. Not only the production activity control becomes more complicated, yield rate will be impacted. As a result, layer cycle time is an input for production control.
5. X-Factor The ratio of production cycle time to theoret-ical process time for each product. With the prerequisite of satisfying the demand of customers, a lower ratio indicates a faster delivery, and a higher capital turnover rate. X-Factor, therefore, is an input in the financial aspect.
6. WIP level The number of lots that has been released into the wafer fab but has not yet been finished processing through all of its manufacturing steps in a period of time. As WIP level increases, more capital is locked, and capital turnover rate decreases in consequence. Therefore, WIP level is an input factor in the financial aspect.
7. Throughput The number of lots of production that passes through the final operation step in a period. A higher throughput implies a higher sales revenue and a higher capital turnover rate for the enterprise. Throughput, as a result, is an output in the financial aspect.
8. Contribution margin The profitability of a certain prod-uct family mix. It is the amount of sales revenue less raw material and indirect variable costs for a period. All finished products are assumed sold. The price for a product is set by its product family, priority rank and the number of layers that product goes through. In a wafer fab, most manufacturing costs are fixed. The indirect variable cost includes cost of all indirect materials and is varied according to the process flow. The higher the contribution margin is, the more pro-ductivity the utilization of system resources is, and the more beneficial the operation of the enterprise is. There-fore, contribution margin is an output in the financial aspect.
4.4. System environment
In order to obtain a set of product family mixes that is efficient for the factory to manufacture, actual data is col-lected from a wafer fabrication factory located on the Sci-ence-Based Industrial Park in Taiwan. A simulation model
is developed by EM-Plant (Tecnomatix Technologies Ltd.,
2001) to generate relevant production performance factors.
Simulation results are then applied in the DEA window analysis to convert the performance results under each product family mix over time into an overall efficiency score. To simplify the complexity of the environment, the simulation model built in this paper is based on the follow-ing assumptions and limitations:
• There are two different product family types. Product family A consists of a variety of logic products, and product family B consists of memory products. The pro-cess of each product family is different and unique. • Products belonging to family A require 305 operations
and pass through the photolithography operation 17 times. Products in family B require 330 operations and pass through the photolithography operation 20 times.
• There are 83 different types of workstations, with 13 6-lot workstations, three 4-6-lot workstations, and 19 2-6-lot workstations. Each workstation consists of a given num-ber of identical machines operated in parallel.
• The lot priority is classed into hot, rush and normal in descending order. The ratio of priorities for each prod-uct family is set to be 1, 2, and 7 for hot, rush and nor-mal classes, respectively.
• Wafer lot(s) can be released to shop floor only when the same quantity of wafers are finished and transferred out. The releasing batch size for both normal and rush lots is
six lots. Batch machines adopt full batch size policy. Once batch forming is completed, processing sequence is based on the priority class and FIFO rule.
• The hot orders are not limited by batching policy, and they can be released into shop floor and be loaded onto any batch machine with only a single lot.
• Lots with different product types and classes cannot be processed simultaneously.
• The charged price for product with normal priority is set to be $40 per passing through the photolithogra-phy operation for product family A, and $50 for product family B. Because the waiting time for higher priority orders is shorter than that for normal orders, the charged prices for hot and rush priority products are set to be 150% and 50% mark-up of the price for normal product, respectively.
Table 2
Throughput targets and average throughput outcomes
Product family mix Monthly throughput target (lot) 420 620 640 464 343 387 526
Mix (2, 8) Real average throughput target (lot) 423 625 637 468 345 388 525
Mix (3, 7) 420 615 645 469 338 392 529 Mix (4, 6) 424 620 645 466 343 392 530 Mix (5, 5) 420 618 642 465 348 392 525 Mix (6, 4) 423 624 645 465 347 382 523 Mix (7, 3) 419 624 641 462 341 387 529 Mix (8, 2) 425 617 635 459 348 390 524 Table 3
Simulation results for candidate factors under Mix (2, 8) Year (throughput target) WIP in front of photolithography workstation (lot) Throughput (lot) BN utilization rate Number of CCR workstations WIP level (lot) Layer cycle time (second) X-factor Contribution margin ($) Year 1 (420 lots) 8 423 0.638 0 187 53,192 1.41 106,149,525 Year 2 (620 lots) 21 625 0.927 8 306 60,043 1.59 156,543,300 Year 3 (640 lots) 26 637 0.963 10 319 61,354 1.63 161,580,325 Year 4 (464 lots) 10 468 0.700 0 206 53,797 1.43 117,118,625 Year 5 (343 lots) 6 345 0.517 0 151 52,422 1.39 86,856,600 Year 6 (387 lots) 8 388 0.577 0 169 52,657 1.40 97,129,975 Year 7 (526 lots) 11 525 0.779 2 236 55,219 1.46 131,401,475 Table 4
Correlation analysis of candidate factors
Throughput (lot) BN utilization rate Number of CCR workstations WIP Level (lot) Layer cycle time (second) X-factor Contribution margin ($) WIP in front of photolithography
workstation (lot)
0.94 0.94 0.91 0.97 0.96 0.92 0.85
Throughput (lot) 1.00 1.00 0.82 0.99 0.89 0.85 0.90
BN utilization rate 1.00 0.84 0.99 0.89 0.86 0.91
Number of CCR workstations 1.00 0.88 0.87 0.85 0.82
WIP level (lot) 1.00 0.93 0.91 0.93
Layer cycle time (s) 1.00 0.97 0.83
• Direct material cost is set to be $100 per wafer. Indirect material cost, such as photo-resist, special gas, chemical and quartz, is varied according to the production family.
The indirect material cost is assumed to be $7.5 per layer for product family A, and $8 per layer for product fam-ily B.
• The observation period is seven years, and the through-put target is set to be 420 lots, 620 lots, 640 lots, 464 lots, 343 lots, 387 lots and 526 lots per month for year 1 to year 7, respectively. The window length is fixed to be three years (K = 3).
• Product family mixes are set between (2:8) to (8:2). Mix (2:8) means that the product family mix ratio for prod-uct family A to prodprod-uct family B is 2 to 8.
• The simulation model is run 15 times to generate statis-tical results under each product family mix and each throughput target.
Table 5
Input and output factors for evaluation
Factor Input or Output
Layer cycle time Input
WIP in front of photolithography workstation Input
WIP Level Input
BN utilization rate Output
Contribution margin Output
Number of CCR workstations Input
X-factor Input
Table 6
Window analysis of alternatives Alternatives Year 1 (420) Year 2 (620) Year 3 (640) Year 4 (464) Year 5 (343) Year 6 (387) Year 7 (526) Mean (Ml) Variance (Vl) TRl Mix(2, 8) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.991 0.9994 0.0006 0.0086 CR1,m X 0 0 0 0 0 X CR1 0 Mix(3, 7) 1 1 0.988 1 0.980 1 1 1 0.995 1 0.995 1 0.995 1 1 0.9970 0.0015 0.0199 CR2,m X 0 0.02 0 0 0 X CR2 0.0199 Mix(4, 6) 0.998 1 0.948 1 0.945 0.990 0.981 0.990 0.973 0.990 0.973 0.999 0.973 1 1 0.9839 0.0049 0.0549 CR3,m X 0 0.036 0 0 0.001 X CR3 0.0358 Mix(5, 5) 0.960 0.985 0.950 0.981 0.950 0.982 1 0.981 0.975 0.981 0.975 0.969 0.978 0.996 0.976 0.9759 0.0038 0.0503 CR4,m X 0.004 0.050 0 0.004 0.027 X CR4 0.0503 Mix (6, 4) 1 1 0.933 1 0.931 0.978 0.984 0.976 1 0.976 1 0.980 1 0.987 0.997 0.9828 0.0061 0.0694 CR5,m X 0 0.053 0.001 0 0.007 X CR5 0.0530 Mix (7, 3) 1 1 0.967 1 0.967 1 1 1 1 1 0.990 0.945 0.990 0.955 1 0.9877 0.0051 0.0545 CR6,m X 0 0.033 0 0.010 0.010 X CR6 0.0327 Mix (8, 2) 1 0.973 0.966 0.973 0.966 1 1 1 1 1 1 1 1 1 1 0.9919 0.0038 0.0340 CR7,m X 0 0.034 0 0 0 X CR7 0.0340
4.5. Results of window analysis
The data of the candidate factors is obtained from run-ning simulation under the environment of the given
throughput target and product family mix.Table 2shows
the monthly throughput targets and average monthly throughput outcomes under different product family mixes in each year. Note that the predetermined throughput tar-gets and the outcomes from the simulation model may not be the same. In order to maintain a fair evaluation, only the simulation results with throughput deviation of less than five batches from the predetermined throughput tar-get are collected. A partial data of the collected candidate
factors under different environments is shown inTable 3.
Based on the procedures stated in Section4.2, a
correla-tion analysis of the factors is done by STATISTICA 6.0
(StatSoft Inc., 1984) to check if there is any factor that
has a negative correlation coefficient or perfect positive correlation with other factors. The correlation coefficient
of the input and output factors are shown in Table 4.
The correlation coefficient between throughput and bottle-neck utilization rate is exactly one. Since the correlation coefficients of bottleneck utilization rate with other factors are higher than the coefficients of throughput with other factors, throughput is deleted from the list. The input and output factors selected for evaluation of the wafer fab are listed inTable 5.
With the simulation results of the selected factors, DEA window analysis can be done by Excel Solver via Visual
Basic application (Microsoft Company, 2003). In this
paper, we assume constant returns to scale; that is, as all inputs double, all outputs will double. The overall
effi-ciency for each DMU is calculated by using CCRd-I model,
and the DEA window analysis is applied. These results are
shown inTable 6.
Observing the average efficiency values, Mix (2, 8) is the highest with a mean of 0.9994. On top of that, this product family has the lowest variance of 0.0006. In a highly variant demand changing environment, Mix (2, 8) has a quite sta-bilized performance over the years.
The second and third best product family mixes are Mix (3, 7) and Mix (8, 2). Both mixes maintain relatively high efficiency over the periods, and their variances are not too big either; therefore, the overall performances of the system under these two mixes are quite stabilized too. Regarding the CR value, the best mix is Mix (2, 8), and the second best is Mix (3, 7). Mix (2, 8) also has the best TR value of 0.0086, followed by Mix (3, 7) and Mix (8, 2).
With the overall evaluation, the best mix is Mix (2, 8), and Mix (3, 7) and Mix (8, 2) perform quite well too. In fact, the performances under Mix (2, 8), Mix (3, 7) and Mix (8, 2) are not significantly different. Therefore, these three mixes are further evaluated. Since financial success is the ultimate goal for an enterprise, only the financial fac-tors, contribution margin, X-factor and WIP level, are
con-sidered here, and the results are shown inTable 7.
Under the window analysis of the three product family mixes by focused on financial aspect, Mix (2, 8) and Mix (3, 7) perform well than Mix (8, 2) in efficiency mean, var-iance and total range. In addition, Mix (2, 8) performs bet-ter than both Mix (3, 7) and Mix (8, 2) in all aspects. This implies that if the fab is able to maintain such a product family mix in a long term, it can be competitive and make a very reasonable profit. In the case that the fab need to be flexible in order acceptable, then it should concentrate its Table 7
Window analysis of the top three alternatives by CCRd-I and CCRd-O
Alternatives Year 1 (420) Year 2 (620) Year 3 (640) Year 4 (464) Year 5 (343) Year 6 (387) Year 7 (526) Mean (Ml) Variance (Vl) TRl Mix(2, 8) 1 1 1 1 1 1 1 1 1 1 1 1 0.9133 0.9126 0.8879 0.9809 0.0107 0.11208 CR1,m X 0.000 0.000 0.000 0.087 0.087 X CR1 0.087 Mix(3, 7) 0.9834 0.9975 0.9583 0.9949 0.9583 0.9929 0.9583 0.993 0.9223 0.9978 0.9223 0.9834 0.8424 0.8975 1 0.9602 0.0123 0.15761 CR2,m X 0.003 0.000 0.005 0.080 0.086 X CR2 0.086 Mix(8, 2) 0.793 0.9731 0.9681 0.9731 0.9681 0.7862 0.9681 0.7849 0.7753 0.7841 0.7753 0.7916 0.7081 0.7227 0.9001 0.8448 0.0268 0.26496 CR7,m X 0 0 0.002 0.067 0.069 X CR7 0.069
product mix in a range from Mix (2, 8) to Mix(3, 7), and preferably Mix (2, 8).
5. Conclusions
In this paper, a DEA window analysis model is estab-lished to evaluate product family mixes in a wafer fab. Without assigning weights to any performance indicator, we can use DEA window analysis to evaluate the efficiency of different product family mixes under a long term and obtain a best product family mix that is relatively more effi-cient for production. The results not only try to maximize the production efficiency and hence the profit, but also con-siders several other important input and output factors that maintain production smoothing.
A virtual wafer fabricator is first constructed, produc-tion with various product family mixes over several peri-ods of time is simulated, and simulation results of critical performance factors are collected. The DEA window analysis is then applied to analyze the results of different product family mixes over time, and the mixes with higher performance are selected. For the selected mixes, another DEA window analysis is run based on a reduced number of factors that are the highest concern of the management, and the most recommended product family mix can be generated as a result. By adopting the pro-posed mechanism, a semiconductor fabricator can have a guidance regarding strategies for order management and aggregate planning to improve manufacturing effi-ciency and to be competitive. For the selected product family mix, how to determine the most appropriate prior-ity mix to both satisfy customer demand and meet fab production performance can be our future research direction.
Acknowledgement
This research is supported in part by Grant NSC 93-2213-E-009-017.
References
Asmild, M., Paradi, J. C., Aggarwall, V., & Schaffnit, C. (2004). Combining DEA window analysis with the Malmquist index approach in a study of the Canadian banking industry. Journal of Productivity Analysis, 21, 67–89.
Atherton, L. F., & Atherton, R. W. (1995). Wafer fabrication: Factory performance and analysis. Norwell: Kluwer Academic Publishers.
Charnes, A., Clark, C. T., Cooper, W. W., & Golany, B. (1985). A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the US Air Force. Annals of Operations Research, 2, 95–112.
Charnes, A., Cooper, W. W., & Rhodes, W. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Charnes, A., Cooper, W. W., Lewin, A. Y., & Seiford, L. M. (1994a). Data envelopment analysis: Theory, methodology, and application. Norwell: Kluwer Academic Publishers.
Charnes, A., Cooper, W. W., & Seiford, L. M. (1994b). Extension to DEA models. In A. Charnes, W. W. Cooper, A. Y. Lewin, & L. M. Seiford (Eds.). Data envelopment analysis: Theory, methodology and applica-tions. Norwell: Kluwer Academic Publishers.
Chung, S. H., Pearn, W. L., & Lee, A. H. I. (2006). Measuring production performance with different product mixes in semiconductor fabricator using data envelopment analysis (DEA). International Journal of Industrial Engineering, 13(1), 5–17.
Cooper, W. W., Seiford, L. M., & Tone, K. (2000). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Norwell: Kluwer Academic Publishers. Ehteshami, B., Petrakian, R. G., & Shabe, P. M. (1992). Trade-offs in
cycle time management: Hot lots. IEEE Transactions on Semiconductor Manufacturing, 5(2), 101–105.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, 120, 253–290.
Fronckowiak, D., Peikert, A., & Nishinohara, K. (1996). Using discrete event simulation to analyze the impact of job priorities on cycle time in semiconductor manufacturing. In 1996 IEEE/SEMI advanced semi-conductor manufacturing conference, pp. 151–155.
Golany, B., & Roll, Y. (1989). An application procedure for DEA. OMEGA: International Journal of Management Science, 17(3), 237–250.
Kang, H.-Y., & Lee, A. H. I. (2007). Priority mix planning for semiconductor fabrication by fuzzy AHP ranking. Expert Systems with Applications, 32, 560–570.
Mahadevan, R. (2002). A DEA approach to understanding the produc-tivity growth of Malaysia’s manufacturing industries. Asia Pacific Journal of Management, 19, 587–600.
Microsoft Company, (2003). Excel. Seattle, USA.
Narahari, Y., & Khan, L. M. (1997). Modeling the effect of hot lots in semiconductor manufacturing systems. IEEE Transactions of Semi-conductor Manufacturing, 10(1), 185–188.
StatSoft Inc. (1984). STATISTICA. Tulsa, USA.
Sueyoshi, T. (1992). Comparisons and analyses of managerial efficiency and returns to scale of telecommunication enterprises by using DEA/ WINDOW (in Japanese). Communications of the Operations Research Society of Japan, 37, 210–219.
Sun, D. B. (1988). Evaluation of managerial performance in large commercial banks by data envelopment analysis, Ph.D. Thesis, Grad-uate School of Business, Austin: The University of Texas.
Tecnomatix Technologies Ltd. (2001). EM-PLANT objects manual. Germany: Tecnomatix Software Company.
Yue, P. (1992). Data envelopment analysis and commercial bank performance: A primer with applications to Missouri banks. Federal Reserve Bank of St. Louis Review, 74(1), 31–45.
