Performance Evaluation of Wafer Fab Operation Using DEA

Transcription

1 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1, pp (2006) 1 Performance Evaluation of Wafer Fab Operation Using DEA Mei-Chen Lo 1,2 and Gwo-Hshiung Tzeng 3,4 1 Department of Business Management, National United University, Miao-Li, Taiwan 2 Institute of Management on Technology, Feng-Chia University, Taichung, Taiwan 3 National Chiao-Tung University, 1001, Ta-Hsueh Rd., Hsinchu 300, Taiwan 4 Kainan University, No.1, Kainan Rd., Luchu, Taoyuan, 33857, Taiwan ABSTRACT Most of the performance assessment of semiconductor manufacturers is based on their selfappraisal or subjective judgments. The need to measure fab operation performance along with its various dimensions have led to the development of numerous quantitative performance indicators. However, an overall scheme to measure the performance of fab operation involving multi-input and multi-effects (output) has not been established. The method of Data Envelopment Analysis (DEA) may meet the above needs. This empirical study uses DEA to build a model to evaluate the performance of semiconductor manufacturing companies in Taiwan, using the input and output data from year 1999 through It is solved for the CCR, A&P, Cross and Multi-Purpose Efficiencies. Both CCR and A&P models are of the self-appraisal type, the Cross model is of the peer-evaluation type, while the Multi-Objective models are of the overall-evaluation type. Furthermore, the CCR efficiency is divided into purely technical (BCC) and scale efficiencies. In addition to a comparison of efficiencies and associated discussions, an analysis of the scale-return is offered. The results are brought up in interviews with experts of the industry. It is concluded that the results based on Cross and Multi-purpose models are more credible and realistic. The performance evaluation method devised accordingly is suitable for adoption. Keywords: data envelopment analysis (DEA), multiple objective decision making (MODM), multiple objective DEA, semiconductor industry, performance evaluation, operation efficiency. 1. INTRODUCTION The semiconductors used in electronic and information products are mainly integrated circuits (IC), which are generally made of silicon wafers. The semiconductor industry in Taiwan predominantly refers to silicon wafer IC production (so called wafer foundry). The Taiwan semiconductor industry has developed since it created the semiconductor dedicated foundry industry in Initially, the funds for developing the Taiwan semiconductor industry mostly come from the government s fund for initial technology development, and are then transferred to private companies for commercial use. Since the government is involved in industrial development, its purpose is to promote the technology level in terms of environment, industry supply chain and infrastructure. The development of Taiwan s electronic technology has already had a significant effect on national economy, and its performance is recognized worldwide. The dedicated foundry business has continued as the world market leader by steadily increasing its capital spending and by outperforming all other market competitors. The need to evaluate the various dimensions of fab operation performance has led to the development of many quantitative performance indicators. However, depending upon the specific indicator examined, different conclusions can often be reached regarding performance. Furthermore, although performance and scale economies are closely related issues, they have generally been examined separately in the semiconductor manufacturing industry. This paper discusses the application of DEA and efficient frontier production functions to investigate two important subjects in fab operations: first, the operation efficiency; and second, the relationship between performance and scale economies. Using data from several production lines over a three-year period, the results indicate that efficiency and effectiveness are positively related. Further, they imply that the magnitude

2 2 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1 (2006) of scale economies depends on the output specifications. Charnes et al. (1978) developed DEA as a methodology to evaluate the relative efficiency of each Decision Making Unit (DMU) with multiple input and output variables, based solely on the observed performance. The original DEA models assume that inputs and outputs are measured by exact values on a ratio scale. However, the measurement scales of input or output variables sometimes are ordinal or interval. To overcome this issue, Golany (1989) assigned weights to output variables and ordered them. DEA is based partially on pairs of units to create the pair-wise comparison matrix. The evaluation tools are used to develop a project, but the overall evaluation model has rarely been evaluated. These tools involve the collection and analysis of large amounts of data to provide relevant and concise information to aid the decision makers who review the performance through fab to fab or line to line. It is always considered a sensitive subject to discuss in public even if the performance diagnosis system becomes crucial for doing an efficient work. Instead of focusing on single factor as of the wafer output quantity or profit margin, top management may use the tools as the feasible way to evaluate the operation efficiency of a wafer fab for reasonable resource allocation and the best customer service. It is strongly suggested to confront this topic and build a fair model objectively. In Section 2, we present the characteristics of semiconductor industry to show the importance of fab performance assessment as facing internal and external changing factors. In Section 3, we present the DEA model and an approach for selecting variables for the analysis. We consider four types of input variables and three types of output variables, as given in our database. In Section 4, we present a series of nonparametric statistical tests to test the consistency of the various ranks and their fitness with the DEA. In Section 5, an empirical study is presented, with the results and analyses. In Section 6, we suggest several ranking methods. Finally, conclusions and suggestions for further research are given. 2. CHARACTERISTICS OF SEMICONDUCTOR FAB OPERATION In this industry, competition is fierce and profits are being squeezed by increased material and labor costs. As a result, efficient fab operation is required to allow for capital improvements. Since in the highly competitive electronics industry all of the increased costs cannot be passed on. Thus, there is a choice between increased productivity and reduced profits. In this situation, the enterprise must purchase capital equipment to reduce the manufacturing costs and look for others ways to become more efficient. As the foundry business is characterized by Yuan et al. (1998), manufacturers improve their productivity to the limit in a fair industry cycle that generates as much as revenue for future expansion need. Then during a recession period the industry integrates internal resources and develops new and advanced technologies to make the next advance market. Though downturns happen frequently in this industry, followed by extended periods of unfavorable business conditions, top management is always looking beyond industry growth and focusing on how best to manage their businesses, both in good times and in bad times. To address some of the concerns regarding data comparability, this paper uses a comprehensive data set containing most fabs operations status over a three-year time period ( ). 2.1 Industrial Cycling This study views the possible objectives that different technology levels of fabs might want to achieve through technology advance, and argues that the nature of these objectives must be accounted for by developing performance indicators. We emphasize: efficiency, effectiveness, and impact. The study offers an impressive number of indicators that can be used to evaluate fab operation performance. Therefore, these indicators are assumed to be adopted in each operation line. Nonetheless, sharing the common resources among sister fabs can be seen as a way of improving operation performance and customer services. Then, fab operations are clustered into homogeneous groups to avoid a misleading size-related bias that would occur if, for example, 6 inch wafer fab with its 0.35~0.5 um technology and 8, 12 inch wafer fab with leading edge were compared. In general, wafer fab operation faces internal and external change where the internal factors of the microenvironment include operation type, finance, marketing, etc. Then, the external factors of the macro-environment may contain of economic change, financial issues, industrial infrastructure etc. However, from 1996 through 2003, the semiconductor industry endured three years of negative growth- 1996, 1998 and Since the data for this study is from 1999 to 2001, the semiconductor industry was facing another industry cycle. Therefore, fab utilization rate of the mature fabs in this empirical study, such as A, B, C, D show how its demand capacity changed completely through 1999, with a slight fluctuation in 2000, and then dragging down to lower utilization (see Table 1). The percentage changes of fab utilization above are calculated from average utilization divided by installed capacity. It reveals that there is redundant capacity during industry cycling as the change percentage is below 100% though lower utilization occurs in the business hard time. Continuing fab investment and restructure business strategy are important at the best timing of this period. The demand forecast was too optimistic and overestimated the growth of capacity demand during

3 M. C. Lo and G. H. Tzeng: Performance Evaluation of Wafer Fab Operation Using DEA 3 Table 1. The status of utilization through Utilization vs. Capacity A-1999 B-1999 C-1999 D-1999 E-1999 F-1999 G-1999 H-1999 I-1999 *Change % 105% 88% 90% 97% 60% Utilization vs. Capacity A-2000 B-2000 C-2000 D-2000 E-2000 F-2000 G-2000 H-2000 I-2000 *Change % 102% 104% 103% 105% 85% 40% 46% 48% 37% Utilization vs. Capacity A-2001 B-2001 C-2001 D-2001 E-2001 F-2001 G-2001 H-2001 I-2001 *Change % 47% 50% 59% 62% 48% 41% 35% 46% 44% Remark: * Change % = Utilization/Capacity the prosperous business in year The manufacturers underwent a new fab (E-1999, F-2000) establishment plus line expansion via acquisition and business merger strategies (G-2000, H-2000 and I-2000). Speedy capacity expansion from merger requires a certain time to integrate internal staff from different cultures. 2.2 Fab Operation Efficiency Assessment Like many industries where output (e.g. perishable goods) is a clearly identifiable entity, the output of a semiconductor manufacturing firm can be quantified in various ways. As characteristic of the foundry business, it is best to work hard in a fairly good economic cycle to gain the needed capital for future expansion. During recession periods it is appropriate to integrate internal resources and develop new and advanced technology to take the next powerful shot in the market. The basic reason for this difference is that the output of a fab operation cannot be stored for future use. Instead, it must be used in the quickly changing cycle of investment. If a wafer fab runs only its half capacity to meet customer demand during a period of time, it cannot use the other half of capacity to produce inventory and then it becomes a waste of resources. This has led to two separate measures of wafer output: yields (often referred to as produced output type ) and technology complication or applications (often referred to as consumed output type ). The Taiwan semiconductor industry is in a highly competitive environment and continuously competes with globalized international businesses, so it must be a technology-driven enterprise from the perspective of effective input and output. We first consider the characteristics of the semiconductor industry in order to construct a systematic structure assessment index for a fab operation. Then, we use various DEA models to conduct assessments based on the data collected, considering both static and dynamic analytical functions. The feedback information obtained from this real case study was provided to decision-makers of each operation fab for their reference for future improvement. 3. BUILDING FAB PERFORMANCE ASSESSMENT SYSTEM As previously mentioned, assessing fab operation performance has been one of the most difficult areas to be investigated within the semiconductor manufacturing industry. Initially, we specify a set of indicators to measure the performance of fab operation, and define the conceptual aspects of this evaluation as: efficiency, productivity, profit, complexity of process, quality of service, etc. Generally speaking, the quantitative indicators of fab performance are wafer output, fab yield and cost, as the productivity indices; while the cycle time and wafer sorted yield indicate the quality of service for foundry fabs. Cost can be measured by manpower; materials and utilities expenses; together with capital invested in facilities, and equipment to achieve certain wafer output and technology implementation. In this paper, the output from manpower is measured as the total income (salary, bonus and others) of employees (operators, engineers and administrative personnel) per wafer output; material is the expense of wafer production, capital is the total number of production tools or chambers operating in the fab, technology mainly states within this study as the process steps of certain process technology so-called stepmove. 3.1 Description of Study Background The study Tzeng et al. (2004) described here covers the three-year period from The authors explored many aspects of DEA s extension to competitive situations, and the application of these extensions to the marketing of semiconductor fab operation. During this period, semiconductor fabs are chosen for this study with a variety of reasons as below: a. When this study was launched in April 2002, the semiconductor industry was undergoing upheaval due to the introduction of many new firms, as well as new technology of 0.13 um and 90 nm. This made the

4 4 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1 (2006) operation challenging and promised some insight into how to evaluate fab operation via the application of DEA which would handle those of changes as of the new technology inbreed, which are usually accompanied by heavy investment in capital and talent. b. The semiconductor industry is characterized by a high degree of competition and intensive investment, resulting in severe pressure on running a wafer fab, even during recession periods. How to efficiently operate a wafer fab includes material and technology implications for the profitability of the product and its manufacturing process. c. Many companies in this industry internationally based, with competition at various hierarchical levels, e.g., at technology, wafer size, product type, cost and expenditure. d. Detailed operating expenditures and running information for this category were available several years ago. These data originated from separate (independent) sources in an empirical case study. Fab operation has become a vital business tool in recent years, against a global backdrop of increasing economic integration and technology competition. In Taiwan, however, the relatively small scale of many enterprises limits their resource to access the comparable and volume of fab operation that they require. The efficiency evaluation through fab operation inside within an enterprise is quite sensible to be appraised in any respect due to involving internal resource allocation and sustaining highly spirits of workforce through whole company. For this reason, it may openly take to fair discussion about the advantage of academic research on the empirical study to assist how to increase the fab efficiency. This may provide local businesses with a comprehensive understanding of what makes efficient fab operation and help strengthen their competitiveness. 3.2 Literature Review and Assessment of Fab Operation Efficiency The main purpose of efficiency assessment is to provide credible and reliable feedback information for decision-makers to revise the direction and contents of their business strategies. The assessment index of fab operation efficiency both help enhance the establishment of an operational system, and also be a blueprint to effectively develop efficiency evaluation within semiconductor industry. The most fundamental issue in exploring fab operation efficiency is to find proper and feasible indices and standards. Accordingly the definition of operation fab efficiency used multiple variable indices. From this study, we found that a single performance index is insufficient to completely illustrate the behavior of operation fab efficiency. The narrow prospective of a single variable limits its capability of illustration, which has consequently led to wide acceptance of the definition of fab operation efficiency with using multiple variables attribution and related studies in this field. There are numerous factors that can increase fab operation efficiency. First of all, a stricter and more objective model for assessment must be developed and a reasonable implementation procedure should be designed so that assessment results can truly reflect both the reasonableness of the operational resources in which operation fabs invest, thus the results produced will provide useful information for decision makers to improve operation performance. In the literature most scholars have employed an all-phase efficiency index to assess the quality of DMUs, but few have included weight distribution of each efficiency (Higgins, 1989). When Bessent et al. (1983) applied DEA to assess relative efficiency of fab operation efficiency and business strategies, they set up the weight for each input and output assessment item. Kao (1994) employed Pareto optimality theory to assess operation fab efficiency in Taiwan and ranked firms with results matching the government s assessment. Charnes et al. (1981) adopted DEA to assess the efficiency of elementary fabs operation and their policies around Boston. Ahn et al. (1989) applied DEA to assess higher education, indicating that DEA is more reasonable and accurate than classical assessment approaches. Most of these studies have conducted field surveys to assess the performance of each DMU. However, they did not consider the difference of each aspect faced when fabs tried to upgrade themselves, such as leading technology implementation, operation environment, applicable operational resources, potential development of fab, and the size of each fab. In 1978, Charnes, Cooper and Rhodes (CCR) extended Farrell s efficiency assessment theory to multiinput and multi-output situations and introduced a mathematical programming model to find the production frontier and the proposed DEA. The input and output items of most for-profit organization can be easily identified and quantified, and there are some functional relation between input and output, so their organization efficiency can be objectively assessed through parametric approaches. However, in non-profit organizations most of the assessment items have multiple criteria and are not easy to quantify. The DEA has very high functional performance and has become the main efficiency assessment approach. In the semiconductor manufacturing field, DEA has the following basic functions: (1) it enables decision makers to conduct analysis from an economic perspective, conducting overall assessment of resource inputs and outputs; (2) during assessment, each item will be properly weighted according to its importance, not subjectively given a fixed weight by an assessing authority according to personal experience; all items are categorized and organized to come up with a total efficiency index; and the characteristics of the organization

5 M. C. Lo and G. H. Tzeng: Performance Evaluation of Wafer Fab Operation Using DEA 5 to be assessed are not considered; (3) compared to a parametric approach, DEA has two major advantages in that there is no need to preset function type or to estimate parameters for the function. In addition, DEA has the following two advantages: (1) it is easier to induce overall and individual assessment indexes for efficiency, and (2) it can clarify the relative efficiency and relative rank for the organization assessed. DEA also meets the ideal quantified assessment model for efficiency prescribed by Lewin and Minton (1986). When considering the model of efficiency measurement, we must return to the issue of the characteristics of semiconductor industry, as well as the manner of fab operations management when facing business cycling. We observe that following the model construction, there is a positive correlation between technical efficiency and the utilization, but a negative correlation between scale efficiency and the utilization of DMUs, despite the fact that these concerns have been accounted for the input and output factors in the model. Thus, it may be important to introduce the industry from other aspect to evaluate the status of the empirical study. 3.3 DEA Framework Currently, DEA is an assessment approach in management science which is extensively used to assess the efficiency of multiple-input and multiple-output systems. There are many successful cases in non-profit businesses such as libraries and public hospitals in addition to forprofit business such as banks and hotels. As is generally known, DEA is a non-parametric approach to efficiency measurement based on Farrell s (1957) original work that was later popularized by Charnes et al. (1978). The model proposed by Charnes et al. (1978) was fairly inflexible in that it assumes constant returns to scale in its production possibility set. Since many real-world applications have returns to scale that are not constant, Banker et al. (1984) developed an efficiency frontier structured by both constant and decreasing returns to scale. In the theory of DEA, a DMU is relatively efficient as long as the combination of input and output from the DMU is within the boundary of DEA; otherwise, a DMU is relatively inefficient since its combination is outside the boundaries. The characteristics of DEA can be summarized as: (1) it can easily handle the evaluation problem of multiple inputs and multiple outputs without facing the difficulty of parameter estimation so it can handle real world problems; (2) it has the characteristic of unit invariance, i.e. changing the scale of input or output quantities that does not alter the results; (3) it calculates a single aggregative index to measure the efficiency that may properly describe the concept of total factors of productivity (TFP) in economics; (4) its weighting factors are generated by mathematical design and free of the influence from human factors that could cause bias during evaluation; (5) it has flexible data processing that can simultaneously handle various data with different dimensions; (6) it can handle the external variances that are based on the data characters of Ratio and Non-Ratio in DEA. Therefore, DEA can evaluate efficiency under difference circumstance of the respective DMUs; (7) it is necessary to collect a great deal of data concerning the production status of the fab. The evaluation indices of the DEA model used in the remainder of this paper are: a. CCR, a global efficiency measure which can be determined by solving a linear programming problem, and which first was studied by Charnes, Cooper and Rhodes (1978). It useful discussion of this subject is in Banker, Charnes and Cooper (1984). b. BCC, an efficiency measure, that assigns an efficiency rating to each of DMUs lies on the efficient production surface, even if it may not be operating at its most efficient scale size. For a detailed discussion, again see Banker, Charnes and Cooper (1984). c. A&P: this index may be interpreted as the maximum possible proportional decrease in the input vector that is required to make the observation efficient. Efficient observations are assigned an index value in the BCCmodel that the index value is equal to or larger than the one in the A&P model (Anderson and Peterson, 1993). d. Cross Model: An analysis examines a neglected aspect of DEA: cross-efficiency. The concept of crossefficiency is developed in a number of new directions. The analysis grounds an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discusses the relative merits of each. It also presents mathematical formulations of, and intuitive meanings for, three possible implementations of aggressive and benevolent cross-efficiency. Two of these formulations have been implemented in computer programs; their performance is compared empirically on a real data set. Finally, the analysis suggests practical uses for cross-efficiency, illustrated with reference to the same data set by Doyle and Green (1994). e. Fuzzy Multiple Objective Programming (FMOP): The conventional approach of DEA analysis considered each individual DMU separately, and then calculated a set of weights, which brought maximal relative efficiency to each group. This approach made most DMUs as efficient as possible. A revised DEA multiple objective programming approach, proposed by Chiang and Tzeng (2000), searched for a set of common weights by calculating all DMU s efficiency ratio. This considers the efficiency ratio of all DMUs in order to calculate and find a set of optimal based weights (identity-based) so that the efficiency ratio of all DMUs calculated accordingly improves as the ratio

6 6 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1 (2006) gets larger, Chiang and Tzeng (2000). To achieve this goal, the concept of multiple objective programming can be employed to find a set of consistent weight combination approach, so that the optimized efficiency value can be calculated for each DMUk in overall relative efficiency achievement. Kuhn and Tucker (1951) is one of earliest considerations of multiple objectives using vector optimization concept, followed by Yu (1973), who proposed a compromise solution method for coping with Multiple Objective Decision Making (MODM) problems. Subsequently, there have many works using compromise optimization methods for applications such as transportation investment and planning, econometric and development planning, financial planning, capital budgeting, business conducting and investment portfolio selecting, health care planning, land-use planning, water resource management, forest management, public policy and environmental issues, etc. Moreover, since Zadeh (1965) originally proposed fuzzy set theory, then he and Bellman (1970) presented the concepts of decision-making in fuzzy environment in1970 that increasingly heuristic approaches have been developed considering the nature of fuzzy metrics and conflicts in practice. Dealing with the MODM problems by a compromise solution typically consist of generating available alternatives, establishing criteria, assessing the criteria weights, and selecting the appropriate ranking method. In such a process, the decision maker (DM) wants to attain more than one objective or goal in selecting the course of action, while satisfying the constraints dictated by environment, process, and resources. Mathematically, these problems can be represented as: Max/Min [f 1 (x), f 2 (x),, f k (x)] s.t. x X, X = {x g i (x) 0, i = 1, 2,, m} (1) where x is an n-dimensional vector of decision variables. This consists of n decision variables, m constraints, and k objectives. Any or all of the functions may be linear or nonlinear, and this problem is often referred to as a vector optimization problem. A further description of the fuzzy multiple objective programming model had referred by Chiang and Tzeng (2000). 3.4 Selection of Input and Output Variables To address some of the concerns regarding data comparability, this paper uses a comprehensive data set containing most of the fab operations reporting for a three-year time period ( ). This type of data set facilitates the examination of both the cross sectional and the temporal properties of the fab operations. Then, to avoid a misleading size-related bias, fab operations are clustered into homogeneous groups. The existence of such a data set can help in addressing the three main concerns frequently voiced in fab operation performance research: first, that analyzing systems of vastly different sizes and operating environments will likely result in parameter estimations that are not representative of the firms in the sample, or are skewed toward the most influential group of firms; second, that most studies based upon panel data include systems of different sizes and configurations that fail to account for the potential differences in performance and scale economies between fabs; and, third, that it is difficult to comparatively evaluate the results from alternative studies that are based upon different cross-sections of fab operations and over different time periods. This study uses a systematic perspective to assess fab operation efficiency; otherwise, researchers ideologies and interests, as well as the models employed could create variation in the definition of input and output. In general, operational index is subjectively selected by the researchers. Selecting indexes by referring to previous research or by a group s Delphi approach to assess efficiency and improve the quality of fab operation is the main relevant approach for semiconductor companies. To broaden operational resources and improve operation efficiency are the two challenges to skillful operations that intend to extend their capacity and develop higher margin product trials. Therefore, the selection of input and output variables must consider relevant benefits and results of these two challenges. The indexes selected in this study cover those indexes mentioned above, and also consider both the feasibility of practical operation and the possibility of obtaining data. The operational input variables consist of four phases that are salary, cost of goods, chambers and stepmove. Fab operations are most likely to produce output by the four input quantities of Manpower (as in Salary), material (as in cost of goods), capital (as in chamber of machines) and implementation technology (as in stepmove). In this paper, manpower is measured as the total salary of employees (operators, maintenance, and administrative personnel); material is measured as the total annual amount of material used as well as the cost of goods used by the fab; capital is the total number of tools or chambers operated by the fab; and technology considers a complex process moving through operations, as in stepmove. Examining the input and output data from this study, and according to the correlation coefficient matrix (shown in Table 2), we find that variables of input and output comply with isotonicity. In other words, the increase of an input will not cause less output of another item. But this is true only if the industry continues capital investment regardless of the down turn period. 3.5 Performance Measurement In the study of a traditional wafer fab, some simple

7 M. C. Lo and G. H. Tzeng: Performance Evaluation of Wafer Fab Operation Using DEA 7 Table 2. Correlation matrix between input and output variables Salary COGS Chamber# Stepmove Patent Margin Wafer Out Salary COGS Chamber# Stepmove Patent Margin Wafer Out evaluation of the relative worth of various decisions is chosen as the objective of the decision-maker. From that point on, the goals and motives are all described by that function. Illustrations of this procedure can be found in traditional economic and management science models. A utility function or a profit function, for instance, is useful mainly because it aggregates a multidimensional phenomenon into a unidimensional one. This is not to say that other factors are never considered; in production theory, for instance, it is generally realized that short-term profit may not be the only motive and that the entrepreneur may also be interested in market share or in discouraging potential competitors. The efficiency assessment conducted in this study is based on the input and output information of each DMU. Both classical DEA and the proposed fuzzy multiple objective DEA are used employed to explore the organizational goal and the selected input and output relation of the 9 operation lines that continually perform capability upgrades, as in the technology driven operation fabs in Taiwan. The samples selected in this study are the 9 operation fab-lines that were performed to the year from 1999 to 2001, according to information from the empirical case study. 4. MEASURE OF ASSESSMENT MODEL This section briefly introduces the traditional assessment model and discusses in detail the characteristic assessment model employed in this study. The assessment models presented in previous publications are as follows: (1) taking the maximum output and deterring the frontier function; (2) estimating the DMU, and (3) comparing the observation values and estimated value to assess the efficiency of DMU. In contrast, this study adopted both the classical DEA proposed by Charnes et al. (1978) and the new DEA Fuzzy Multiple Objective Programming (FMOP) approach proposed by Chiang and Tzeng (2000) to conduct assessment of relative and absolute rank for comparing and analyzing the results. 4.1 The Selection and Application of DEA Analysis Model The input/output factors are examined and selected, then the DEA patterns are chosen to be engaged in the analysis. In addition, this study adopt CCR model, A&P model, Cross model, and FMOP to resolve the efficiency value, which uses the BCC model to associate with CCR model in order to calculate for each DMU the overall technical efficiency, pure technical efficiency and scale efficiency. Because the calculation process is complex, we use the LINGO computer package and DEA-Solver Software to determine the related efficiency values and correlation coefficient from the SPSS computation. We also use EXCEL to solve the fuzzy DEA pattern of multi- goals programming and the general computation. In this CCR model, a value equal to or greater than one indicates relative effectiveness while a value less than one is regarded as relatively inefficient. In the A&P pattern, the effective DMU itself will be removed from the reference set of CCR model. So it may cause the efficiency value changes from 1 to greater than 1. CCR model uses self-appraisal approach to evaluate the efficiency of DMU that the result may be controversial because the appraisal method is subjective without comparing to other DMU as reference. Such DMU will be exposed and excluded from the group of DMU with outstanding performance as the Cross model is applied that uses peer-appraisal approach. On the other hand, it is found that the appraisal result is closer to the reality as FMOP model is applied that uses all appraisal approach. In order to strengthen the discriminate analysis, traditional CCR Model avoid having too many effective DMU, since that makes it more difficult to judge the quality. Frequently these models extract λ j using of the antithesis pattern. The value of all DMUj that corresponds the values unequal to zero by means of receiving reference set appraisal to the unit. Therefore, when a DMU appears in another DMU s reference set, the intensity (Robustness) of DMU effectiveness is stronger as it occurs more frequently. If an effective DMU has never appeared in any other DMU s reference set, it may regard as an outlier which efficiency value is 1, but there exists a differential variable which value is greater than 0.

8 8 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1 (2006) Table 3. CCR, BCC, A&P score and reference sets DMU CCR BCC A&P CCR Referred Set CCR Referred Frequency A B ,7 0 C ,7,8,9 0 D ,9,15 2 E ,4,6,9,15 0 A ,6,9,15 6 B ,6,9,15 7 C ,8,9 2 D ,9 17 E ,7,9 0 F ,15,18 0 G ,7,9 0 H ,9 0 I ,9,15 0 A B ,7,9 0 C ,9,15 0 D ,15,18 3 E ,9,15 1 F ,15,18,19,22 0 G ,15 0 H ,15 1 I , Operation Efficiency Measure Static analysis is the analysis of the management efficiency of a fab in a certain year, using the information from and according to the input and output information listed in Table 3. For this, the current study uses a CCR model for assessment. The results shown in Table 3 are the operation fab rankings, which are sorted by their relative efficiency value and the frequency that the individual operation fab was referred. When the efficiency value is equal to 1, that means the relative effective rates among the 23 DMUs are above the efficiency frontier and therefore they themselves are the reference group. For those Operation Fabs whose efficiency value is less than 1, their reference group is those above the efficiency frontier. Taking B-2001 for example, its reference group includes A-2000, B-2000 and D Each reference group is the examples from which an individual DMU should learn in order to achieve higher efficiency. The more times an efficient group is referred to indicates that it has higher management efficiency and is listed as the example for those DMU with less relative efficiency. Based on CCR assessment, there are 7 Operation Fabs that have higher relative efficiency: A-1999, A-2000, B-2000, C-2000, D-2000, A-2001 and D Three of those DMUs have significantly been referred: the D-2000, considered the best, was referred to 17 times; and the next is A-2001,which was referred to 14 times, followed by A-1999, referred to 13 times. In addition, there are 13 DMUs with no record to be referred: B-1999, C-1999, E E-2000, F-2000, G-2000, H-2000, I-2000, B-2001, C-2001, F-2001, G-2001 and I Based on the BCC assessment (as Table 4), there are 8 DMUs that have higher relative efficiency: A-1999, D-1999, A-2000, B-2000, C-2000, D-2000, A-2001 and D Three of those DMUs have significantly been referred: of these, B-2000 is considered the best, referred to 12 times; followed by A-2000, which was referred to 10 times; and then D-2001, which was referred to 9 times. In other words, these three units have significant Table 4. BCC frequencies in reference set Peer set Frequency to other DMUs A D A B C D A D

9 M. C. Lo and G. H. Tzeng: Performance Evaluation of Wafer Fab Operation Using DEA 9 Table 5. Relative efficiency of the fab operation Rank DMU Aggregate Technical Scale Efficiency Status of Return to Efficiency (AE) Efficiency (TE) (SE) Scale (RTS) 1 A CRS 1 A CRS 1 B CRS 1 C CRS 1 D CRS 1 A CRS 1 D CRS 8 B CRS 9 D DRS 10 B CRS 11 C DRS 12 C CRS 13 I IRS 14 E CRS 15 G CRS 16 H CRS 17 E CRS 18 F CRS 19 F CRS 20 E CRS 21 H CRS 22 I CRS 23 G CRS Remark: IRS: Increasing Return to Scale; CRS: Constant Return to Scale; DRS: Decreasing Return to Scale. technical efficiency, including fab yield management, tool dispatching system, tool layout, incentive programs, response system, etc. to fulfill the requirements of fab operation, as well as responding to business strategies. 4.3 Measurement of Scale Efficiency Management efficiency can be divided into technical efficiency and scale efficiency; that is aggregate efficiency is equal to the product of technical efficiency and scale efficiency. If DMU could realize its status of return to scale, decision makers would know if the scale should be expanded or reduced. If return to scale is in the stage of increasing, decision makers should consider expanding the scale to increase management efficiency. On the contrary, if return to scale is in decreasing, decision makers could consider reducing the scale to increase management efficiency. The analysis of return to scale shows: In terms of fab operation If all other conditions in Table 6 are unchanged, expanding the scale of management for I-2000 could improve their management efficiency. Partitioning Pareto Optimal Unit (POU) and Pareto Non-Optimal Unit (PNU) by aggregate efficiency, the aggregate of POU is 1 and PNU is less than 1. As shown in Table 5, there are seven DMUs: A-1999, A-2000, B-2000, C-2000, D-2000, A-2001 and D-2001, that achieved POU and both were ranked as No. 1. These DMUs achieved Pareto optimal organization, although this does not mean there is no room for them to improve. Because DEA is a concept of relative comparison, therefore, if one of the 7 DMUs has improvement in some area, the assessment grade could be less than 1 and become Pareto non-optimal organization. The rest of the 16 DMUs are PNU and were ranked according to their aggregate efficiency fraction. Only I-2000 is in the stage of Increasing Return to Scale (IRS), but two of C-1999 and D-1999 are in the stage of Decreasing Table 6. Return to scale (RTS) RTS Efficient Projected Total No. of IRS No. of CRS No. of DRS Total

10 10 International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 2, No. 1 (2006) Return to Scale (DRS) both in Taking E-2000 as an example, its aggregate efficiency is ; hence it is a Pareto non-optimal organization. Its technical efficiency is , which means its management efficiency needs to be improved. Its scale efficiency is , which means it did not effectively utilize the available resources, and therefore it needs to re-organize how it utilizes its available resources In terms of the scale of fab operation Among these fabs, the three DMUs, C-1999, E-1999 and F-2001, have their scale efficiency over one. And only C-1999 will need to consider decreasing scale utilization, while E-1999 and F-2001 maintain constant scale utilization. In the event of over-expansion, the decision makers of these operation fabs may try to improve operational efficiency by economizing on the resources of those DMUs. As for those of efficiency scale below 1 but still remain in the stage of Constant Return to Scale (CRS) such as E-2000, F-2000, G-2000 and H On the contrast, it can be explained as of the background of business cycling and fewer resources can be utilized then. Table 6 shows that the study object has normal operation efficiency with the most portions of 21 of the 23 units having positive RTS, even challenging the uncertainty of business cycling and internal factors then. In reality, its performance still keeps in superior competitiveness through the industry wide. Taking G-2000 for example, its aggregate efficiency is Its technical efficiency is which means that their management needs to be improved on operation efficiency. Its scale efficiency is which means that they did not effectively utilize the available resources, so they need to reprogram how they utilize their available resources. 4.4 Efficiency Achievement Measure and Comparative Analysis Taking samples from the DMUs in Taiwan that have been operated efficiently, this study conducted comparative analysis for classical DEA efficiency measure and Fuzzy Multiple Objective Programming (FMOP) efficiency measure to provide statistical data from real DMU (with year) Table 7. Result of the assessment of management efficiency Classical DEA Efficiency Measurement Fuzzy Multiple Objective Programming (FMOP) CCR A&P Rank MaxMin (alpha) Rank Ranking Deviation A B C D E F G H I

11 M. C. Lo and G. H. Tzeng: Performance Evaluation of Wafer Fab Operation Using DEA 11 cases. Comparing the rank of the results, DMUs that have larger gaps, and DMUs that have better efficiency performance were made as follows: Efficiency achievement Efficiency achievement contains the efficiency ratio of the relative achievement of the DMU being assessed. The efficiency achievement measure is calculated by the optimal weight (u * r, v * i ) for each DMU. Table 7 shows the results of analysis on efficiency achievement measure, in which is the optimal weight (u * r, v * i ) was adopted to assess the efficiency of each DMU. The classical DEA shows that the A units, which are A-1999, A-2000 and A-2001, have exist more efficient performance. The resulting performance indices show that the content of input and output ratio are relatively higher than others. The FMOP method uses optimal weights to determine the ranking on a basic level to extinguish each DMU on different performance. Thus, both classical DEA and FMOP indicate that DMU has existed its own explanation of its input-output background that can reasonably be revealed from its different ranking. From the perspective of efficiency measure by classical DEA and FMOP, the results shown in Table 7, the following DMUs are in the classical DEA category of efficient with h k = 1. A-1999, A-2000, B-2000, C-2000, D-2000, A-2001 and D-2001; whereas the other 13 DMUs including B-1999 (h k = ), E-2000 (h k = , and F-2001 (h k = ) are not efficient. Applying the efficiency achievement FMOP model, only two DMUs turn out to be relatively efficient, among then A-1999 (α k = 1), and A-2001, while the other subject DMUs are relatively inefficient. This approach is similar to De Novo programming (Zeleny, 1986, 1995), which can break through the barriers of Pareto s solution and provides more room for further development. On the other hand, the relative efficiency ratio resulting from efficiency measure is the comparative absolute value among DMUs being assessed. When the efficiency ratio is 1, that indicates the performance of the DMU is relatively efficient, which can clearly show which group has better performance. The value of relative efficiency, in addition to being used for ranking, represents for the performance of aggregate efficiency. Furthermore, from the reference set, examples can be made for those DMUs that are relatively inefficient to learn. Also, slack variables analysis of the model to examine the efficiency of the employment of each resource, can provide more information for decision-making. By the FMOP measure, we can further find that thirteen DMUs including C-1999, E-1999, A-2000, B-2000, C-2000, D-2000, E-2000, F-2000, G-2000, I-2000, A-2001, D-2001 and F-2001 were relatively inefficient compared to A-1999, B-1999, B-2001, G-2001, H-2000, H2001 and I-2001 as of its down grade of deviation with much differences. This provides more accurate results for comparing the relative efficiency ratio and absolute achievement ratio Rank comparative analysis Ranking semiconductor operation fabs in terms of efficiency is very frequent in practice since it can push higher output and arouses work morale under incentive programs. However, the very same set of operation fabs can be ranked in different ways at a given time depending on the individual unit performing the ranking. These differences are caused by different understandings and explanations of operation efficiency; and consequently, different importance may be given to particular criteria and different ranking methods may be chosen. This study applied cluster analysis after normalizing the information to categorize the 23 DMUs into five groups by their characteristics, as shown in Table 8. The effectiveness of efficiency ranking obtained from both efficiency achievement measure and FMOP efficiency measure are quite different. From the ranking in Table 8, we observe that only 1 DMU, D-1999, has exactly the same rank; whereas the ranking of the eight DMUs, A-1999, B-2001, H-2001, I-2001, G-2001, Table 8. Rank comparison analysis for DMUs efficiency measurement DMU Rank Ranking Classical DEA FMOP Deviation A A A B B B D D D C H C H I I C G G E E E F F