Fuzzy Integral Analysis for Proactive Strategies in the Semiconductor Foundry Business Mei-Chen Lo(1), Jerzy Michnik(2) and Jonathan C. Ho(3) 1. National United University, Taiwan 2. The K. Adamiecki University of Economics in Katowice, Poland 3. Yuan Ze University, Taiwan ABSTRACT The wafer foundry is a highly competitive business and is subjected to continuous technology innovation. Their services enable integrated circuit (IC) design firms to produce products at low costs with high quality. Being the technological leaders in semiconductor manufacturing processes, wafer foundry companies frequently spearhead process advancements by skillfully leveraging its own R&D resources and the world-class expertise of its material suppliers, IC designers or service alliance partners. This study analyzes the important attributes to operating an efficient wafer foundry fabrication (Fab) and empirically tests the attributes with a selected case. The proposed approach uses fuzzy integral and a simple additive weighting (SAW) method to assign weights. Experts, including internal employees, varied groups of experts and leaders were organized to facilitate the research process. INTRODUCTION Integrate circuit (IC) is the heart of the electronic industry and is the driving force of many technological progresses. The supply chain of IC devices includes IC design, mask making, IC manufacturing, assembly and testing. The supply chain spread all over the world such that IC is a trans-national industry with the characteristics of capital intensive and technology intensive. Many of the new designs from IC design companies and integrated device manufacturers (IDMs) will go into production via setting order to foundry for manufacturing wafer. To avoid expensive manufacturing facilities, many IC design firms have selected to be fabless firms who leave the manufacturing activities to foundries. The semiconductor manufacturing industry is a capital-intensive industry and its technologies upgrade rapidly (Yuan et al., 1998). For a sustainable growth rate in semiconductor industry, cost reduction, superior customer service, and effective communication and information sharing within the firm are critical. Besides, successful market player must look at the application of its process technologies, although the integration of technologies and market imposes difficulty to move forward productivity and the possible output. Still the market-driven force leads the direction of investment. The purpose of this study is to develop an analytical method for technology management and decision-making in the industries with environment which is characterized by rapidly changing technology, shortening product life-cycle, innovative activities in information quality and knowledge management (Tzeng et al., 2005b). The study uses combined qualitative and quantitative approaches to strategic management process and intend to obtain deeper insight into semiconductor business. With the developed methods, various strategies and their related attributes are collectively weighted for their importance. Methodologically comparison of various methods and approaches can shed some light to their characteristics and abilities to solve certain management issues. The method used in the study is proven to be a useful tool for practical decision-making. HIERARCHICAL MODEL OF BUSINESS PERFORMANCE EVALUATION The main goal of the hierarchical framework is the performance evaluation of the semiconductor companies. Four dimensions under this goal are established from the economic viewpoint: the enterprise aspects, the market aspects, the environment and the prospects. The hierarchical structure, adopted to deal with the problems of semiconductor companies’ assessment, is shown in Figure 1. Weights reveal the importance of aspects, criteria and sub-criteria in view of the factors of considered business strategies. They have been obtained as the averages from 20 experts. G oal A sp ec ts C r ite r ia C1 The Enterprise (0 .2 6 3 ) C2 The Market The Factors Considered for Business Strategies C 1 1 S tra te gic A d va n ta ge (0 .3 2 9 ) C 1 2 C o m p e titiv e C o m p e te n c e (0 .3 4 1 ) C 1 3 O p e ra tio n R e sp o n se (0 .3 3 0 ) C 2 1 M a rk e t S tra te g y (0 .5 1 3 ) C 2 2 In d u stry L in k (0 .2 5 2 ) C 3 T h e E n v ir o n m e n t (0 .2 4 7 ) C 4 T h e P r o sp e c ts (0 .2 3 8 ) (0 .4 8 7 ) S u b -C r ite r ia (A ttrib u te s) C 1 1 1 D iffe re n tia tio n (0 .3 2 7 ) C 1 1 2 C o m p e titive A d va n ta g e (0 .3 6 4 ) C 1 1 3 N a m e R e c o gn itio n (0 .3 1 0 ) C 121 C 122 C 123 C 124 S e rv ic e & S u p p o rt ( 0 .2 6 2 ) M a rk e t S h a re (0 .2 5 6 ) A b ility to P ro m o te (0 .2 4 0 ) S ta yin g P o w e r (0 .2 4 2 ) C 1 3 1 O p tio n s to A b a n d o n (0 .3 0 4 ) C 1 3 2 P ro p e n sity to A tta c k (0 .3 2 0 ) C 1 3 3 S p e e d o f R e sp o n se (0 .3 7 6 ) C 211 C 212 C 213 C 214 C 215 M a rk e t L ife C yc le (0 .2 0 5 ) M a rk e t G ro w th R a te (0 .2 0 4 ) M a rk e t S e gm e n ts (0 .1 9 5 ) W a ys to O b ta in (0 .1 9 6 ) A d v a n ta g e (0 .2 0 0 ) C 221 C 222 C 223 C 224 T h re a t o f S u b stitu te s (0 .2 6 4 ) D istrib u tio n C h a n n e ls (0 .2 3 7 ) D e p e n d a b le S u p p lie rs (0 .2 4 9 ) E a se o f S w itc h in g (0 .2 5 0 ) C 31 C 32 C 33 C 34 C 35 G o v e rn m e n t A c tio n ( 0 .2 0 5 ) D e m o gra p h ic s (0 .1 8 3 ) T e c h n o lo g y (0 .2 2 0 ) C u ltu re (0 .1 8 4 ) E c o n o m y (0 .2 0 8 ) C 41 C 42 C 43 C 44 C 45 P ric e S e n sitivity (0 .2 0 6 ) N e g o tia tin g S tre n gth (0 .2 1 7 ) Im p a c t o f F a ilu re (0 .1 9 3 ) R isk o f P u rc h a se (0 .1 9 1 ) P ric e A w a re n e ss (0 .1 9 2 ) Figure 1 Defuzzified and Normalized Weights (Average of 20 Experts) The rich content of our hierarchy makes the classical AHP pair-wise comparisons too laborious for interviewed persons; it could make worse a quality of the results. As the experts are highly experienced (long average service in the field) we assumed that they were able to set direct weights reasonably. For both, criteria importance (weights) and satisfaction, we use fuzzy triangular numbers for evaluation. To assess criteria importance, the interviewed experts were allowed to use fuzzy triangular numbers from interval [1,9] with accuracy of one decimal digit. No limits on membership functions were imposed except the obvious ascending order of lower bound, the most possible value and upper bound. For satisfaction, the only difference was in the interval, which was [1,10] in that case. Before subsequent calculations, the defuzzification of input data was performed with the COA (centre of area) method. From Table 1, the satisfaction upon current circumstances, has been located to each sub-criterion by experts. On this basis the synthetic performance value (SPV) has been figured out as the weighted sum of values of satisfactions. Similar procedure was performed for two higher levels in hierarchy. The results suggest that the business strategy effectively enters in work field; they also illustrate that the identical groups in the various units sustain their unique characteristic. It can be clearly seen that there is much room (overall result 6.24 of 10) for improvement (Table 1). Especially, overall performance measures in the categories (professional groups and areas), show average consistent results for the top five alternatives, indicating that C133, C112, C132, C113 and C111 are the items which need most improvements. According to our results, domestic and non-domestic subjects demonstrate the different way of view how the global businesses are implemented in practice. The market planning and positioning are important issues when company considers its cross-boundary stand-point (position). Differences between the non-domestic and domestic view of business strategies can be explained by different environment and focus, which can affect directly the speed-to-market and potentiality of regional business development. During the recession time, top management tends to view potential opportunities in wide and review internal capability for preparing next fight of new business cycling. It is the reason that top management provides different priority on viewing business strategies. Table 1 SPV by Professional Groups/Areas Categories The Enterprise C11 C12 C13 Overall SPV 0.32 (3) 2.05 (2) 0.35 (1) 2.35 (1) 0.33 (2) 1.88 (3) The Market C21 C22 0.51 (1) 3.14 (1) 3.24 (1) 0.49 (2) 2.97 (2) 2.40 (2) 2.94 (1) 2.94 (2) 3.68 (1) 2.83 (2) 2.99 (1) 3.55 (1) 2.68 (1) 2.82 (2) 2.99 (2) 2.57 (2) Business Strategies C1 C2 C3 C4 0.27 (1) 0.25 (2) 0.24 (3) 0.24 (4) 1.58 (2) 1.52 (3) 1.59 (1) 1.38 (4) 1.62 (2) 1.46 (3) 1.70 (1) 1.35 (4) 1.89 (1) 1.74 (2) 1.14 (4) 1.32 (3) 1.57 (3) 1.39 (4) 1.68 (1) 1.64 (2) 1.88 (1) 1.68 (2) 1.50 (3) 1.43 (4) 1.40 (3) 1.31 (4) 1.65 (1) 1.41 (2) 6.27 4.88 6.13 5.64 6.40 5.06 SPV (Rank) Total Weight SPV 1.69 (1) 1.53 (2) 1.52 (3) 1.51 (4) 6.24 Fab Operation Marketing Operation Support 1.96 (3) 1.95 (3) 2.21 (2) 2.22 (1) 2.14 (1) 2.31 (1) 2.17 (2) 1.95 (2) 2.08 (3) Top T G Manager 1.89 (3) 2.26 (2) 1.68 (3) 2.02 (2) 2.53 (1) 1.78 (2) 2.04 (1) 2.15 (3) 1.93 (1) Rank (1) (4) (2) (3) (1) (2) Remark: “T” stands for Domestic company, “G” stands for non-domestic company. Due to the specificity of the industry, the group of fab operation reveals the highest SPV in comparison with others (Table 1). As wafer foundry business presents a high technology and professional services in the field, so the operation efficiency and marketing implementation in the industry contains a certain vision of exercising business strategies. The weight and the overall SPV point on the enterprise as the most important aspect. The three of the professional groups agree that the environment as well as technology development are superior to the others aspects. They also think that the technology driven force via the strategic technology collaboration is the best way to push the foundry business forward. In view of the market, market strategy distinct from industry linkage, market segmentation is to be drawn for satisfaction of customer needs. To continue implementation of the strategic industry competition-cooperation model can help industry survival. PROACTIVE STRARTEGIES ANALYSIS In our case the role of alternatives are played by strategies. The nine strategies were considered: S1: Cost Control: cost control on operation activities; S2: Marketing and Sales: marketing and selling skill in each aspect of the marketing mix, market research and new product development, market network and sales point (REP, globalization service center, logistic service, maintenance support, etc.), training and skills of the sales force; S3: Quality Activities: quality driven on operation oriented processes and product diversification (yield improvement, output, utilization and efficiency); S4: Innovation and Knowledge Management: knowledge based activities and mechanism-information quality, information technology and innovated knowledge management; S5: Customer Services and Support: to fulfill customers’ satisfaction and focus on customers’ requirement on application, product, market, regional exploration, strategic business unit, advanced technology; S6: Technology Development and Integration: technology driven on development and integration (leading edge)—R&D capability, patent, copyrights, in-house capability in the research and development process (product research, process research, basic research and development), access to outside sources of research and engineering (e.g., suppliers, customers, contractors), R&D staff skills in terms of creativity, simplicity, quality, reliability; S7: Talent incubation and human resource development: flexibility on business strategies – manufacturing, marketing and technology development; S8: Corporate resources integration and allocation: resources rearrangements and reasonable allocations (production and logistic); S9: Capital management and financial risk management: Cash flow, short- and long-term borrowing capacity (relative debt/equity ratio), new equity capacity over the foreseeable future, financial management ability, including negotiation, raising capital, credit, inventories, and account receivable. The evaluation of strategies was based on the numerical values from the interval [0, 10] with accuracy of one decimal digit. This scale was designed to represent intuitive expert’s judgment as follows: the medium point of the scale (5.0) represents the neutrality of a strategy towards given attribute. Values to the left of 5.0 represent the level of negative influence of strategy on given attribute with the highest negative influence given by 0.0. Accordingly, values to the right of 5.0 represent the level of positive influence, with the highest possible value equal 10. With the assumption of independence of the criteria we can use the additive measure for calculating the overall evaluation of alternatives. The SAW has been chosen for this task. More general, we can take into account some level of dependence between criteria. In this case use of non-additive MCDM method such as fuzzy measure and Choquet fuzzy integral for joint evaluation of the alternative is reasonable. For more profound comparison, the other method – experts’ intuitive judgment – has been included. According to a definition of fuzzy integral (Appendix) the parameter λ need to be determined. For every evaluator, λ - value was calculated. The assignment of λ to our hierarchy is as follows: Level 1: λ10 – (C1-C4). Level 2: λ6 - (C31-C35), λ7 - (C41-C45), λ8 (C11-C13), and λ9 - (C21-C22). At Level 3: λ1- (C111-C113), λ2h - (C121-C124), λ3 (CC131-C133), λ4 - (C211-C215), and λ5- (C221-C224). The overall λi -value is obtained (i=1,2,…,10) by using the arithmetic averages from all experts input values. λi -values for different professional categories and overall λi -values are listed in Table 2. λ -value λ1 Table 2 λ - Values for Fuzzy Integral λ2 λ3 λ4 λ5 λ6 λ7 λ8 λ9 λ10 Fab operation -0.992 -0.999 -0.916 -1.000 -0.929 -0.998 -0.994 -0.998 -0.980 -0.999 Operation Support -0.998 -0.999 -0.998 -1.000 -0.994 -1.000 -1.000 -0.997 -0.988 -1.000 Marketing -0.999 -0.998 -0.999 -1.000 -1.000 -0.996 -1.000 -0.998 -0.988 -1.000 Top management -0.645 -0.768 -0.986 -1.000 -0.991 -0.996 -0.999 -0.999 -0.962 -0.999 Overall -0.973 -0.994 -0.986 -1.000 -0.994 -0.999 -0.999 -0.995 -0.971 -0.999 According to Table 2, λ - values appear negative in all cases from different categories of experts. In this case the influence of improving the criteria with lower score is weakened by the effect of non-additivity. ANALYSIS RESULTS AND COMPARISONS The results analysis provides a picture of the strategies comparison. It describes the analysis result from SAW, fuzzy integral and experts’ intuition evaluation. Comparisons of solutions received with different methodologies give the deeper insight into the evaluation process and the opportunity to attain more objective view of the studied problem. Various methods and approaches reveal its own unique characteristic and feasibility of explanation in business strategies as well as the ability to solve practical management problems. The higher evaluation 7.9 given by fuzzy integral in comparison to SAW value 6.1 (Table 3), can be enlighten according to the generic characteristics of these two methods. The large value of fuzzy integral calculation is the combined effect of the sign of λ - value and the normalization. When sum of input weight is greater then 1, λ is negative and lower the fuzzy integral value, but normalization used for SAW, lower the weighted sum even stronger. It may be symptomatic that the experts’ intuition evaluation lies in between the two. C11 Fuzzy Integral S1 6.209 S2 7.610 S3 6.566 S4 8.120 S5 6.946 S6 8.595 S7 7.358 S8 6.170 S9 5.880 Strategy Effect SAW S1 S2 S3 S4 S5 S6 S7 S8 S9 Strategy Effect C12 Table 3 Comparison of the Results C13 C21 C22 C3 C4 C2 Overall 7.693 8.280 6.624 6.924 9.113 8.083 7.834 6.299 5.725 5.867 6.574 4.974 8.974 7.780 6.773 6.697 7.565 7.443 7.402 7.978 5.969 8.046 7.338 8.642 5.869 6.245 5.129 7.239 6.530 5.447 6.612 6.806 7.680 6.025 5.577 5.351 7.787 7.441 5.755 7.201 5.412 7.363 6.635 6.574 7.540 8.443 7.654 6.368 6.521 5.847 6.927 6.044 6.266 7.372 7.447 8.147 6.575 8.796 8.880 8.470 7.741 7.346 7.172 7.378 7.770 5.894 7.840 7.261 8.504 5.994 6.149 5.307 8.283 (4) 8.083 (5) 6.525 (9) 8.624 (1) 8.583 (2) 8.466 (3) 7.549 (6) 7.215 (8) 7.491 (7) 6.0 7.1 7.0 8.3 6.4 8.1 7.1 7.4 6.6 7.9 5.784 7.334 6.563 6.768 6.489 7.553 6.095 5.778 5.227 6.464 7.119 6.273 6.079 7.921 7.383 6.615 6.313 5.443 5.256 6.317 4.897 7.663 5.980 6.414 5.803 5.950 6.278 6.227 7.214 5.446 6.597 6.402 7.431 5.158 5.754 4.799 6.281 5.451 5.770 6.164 4.998 6.140 5.511 5.638 5.150 5.908 6.437 4.855 6.341 4.840 5.432 6.232 5.575 5.926 7.400 6.285 5.862 6.712 5.834 6.110 4.926 6.024 6.712 5.849 6.924 5.914 6.820 6.824 7.119 6.181 6.022 5.648 6.253 6.359 5.603 6.387 5.721 6.805 5.329 5.698 4.970 6.337 (4) 6.510 (2) 5.567 (9) 6.569 (1) 5.825 (6) 6.386 (3) 5.674 (8) 5.833 (5) 5.802 (7) 6.4 6.6 6.1 6.1 5.7 5.7 6.2 6.4 5.9 6.1 5.875 8.250 6.250 7.625 7.125 7.500 6.625 7.125 5.750 6.750 6.625 6.250 7.375 6.000 6.750 6.375 7.250 6.500 5.125 6.375 5.125 6.125 5.125 6.000 6.625 6.000 6.875 7.625 6.625 6.375 8.000 6.500 7.250 6.750 6.625 7.188 6.590 7.488 6.055 8.006 7.946 7.817 7.296 6.678 6.349 7.320 7.254 5.708 7.329 7.072 8.161 5.947 5.911 5.240 6.750 (9) 7.563 (3) 6.875 (6) 8.125 (1) 6.875 (6) 8.125 (1) 7.275 (5) 7.438 (4) 6.788 (8) 6.7 6.6 6.2 6.7 7.1 6.7 7.2 Expert's Intuition Evaluation S1 6.150 8.125 6.250 S2 7.250 7.625 5.750 S3 6.375 7.125 6.000 S4 7.250 7.375 7.625 S5 6.250 7.688 7.000 S6 8.000 8.213 6.875 S7 5.625 6.625 7.125 S8 5.750 6.375 7.438 S9 6.750 5.688 6.438 Strategy Effect C1 6.3 6.9 6.7 Table 4 demonstrates very strong consistency among different methods of strategies evaluation. Innovation and knowledge management (strategy S4) receives the first place independently of the method used. Well-established platform for information transmission and knowledge management is important for building effective databank within a knowledge pool. Due to pure foundry business have operated in Taiwan over 18 years (since 1987), the business models also shift along learning curve, to the point in which maximum output (for lowering cost), yield control (max. fab yield and product yield), production control (higher utilization and lower machine down-time), on-time delivery (min. product cycle time) ensure operation activities and allow to reach business plan. In addition, financial concepts about capital composition may impact long-term business plan. Table 4 Ranking Comparisons from Different Models Strategies S1: Cost Control S2: Marketing and Sales S3: Quality Activities S4: Innovation and Knowledge Management S5: Customer Services and Support S6: Technology Development and Integration S7: Talent Incubation and Human Resource Development S8: Corporate Resources Integration/Allocation S9: Capital Management and Financial Risk Management Fuzzy Integral SAW Experts' Intuition 4 5 9 1 2 3 6 8 7 4 2 9 1 5 3 8 6 7 9 3 6 1 6 1 5 4 8 SUMMARY Strategic decision-making is an extremely complex and difficult process. Many paradigms are developed for strategic decision-making. Most of these paradigms suggest that the strategic management process, both at corporate and business levels, should include industrial evolution, strategy evaluation, environmental analysis, goal setting/formulation, strategies formulation, strategy implementation, strategy evaluation, and strategy control. Most of these processes are complex and unstructured. This research, applying the analytic hierarchy process, structures the complexity relations among essential attributes, criteria, and aspects in a model. The model allows decision makers to analyze strategic alternatives and their supporting attributes in a systematic manner. Rather than using pairwise comparison method, which is typically used in AHP, this research compared three data collecting methods, namely fuzzy integral, SAW and expert intuition. Various data obtained with the three approaches provide more powerful explanation than the traditional approach. The developed methods are applied to semiconductor foundry business as an empirical case. It shows the capability of facilitate decision-making process at strategic level. With minor modification of the model, the methods are applicable to other industries with similar technological and market challenges to the case industry. Selecting and evaluating of the three approaches therefore would depend on the nature of the application and the judgment of the decision maker. Further empirical studies of these methods in other industries can be carried out in the future. REFERENCES Chen, T.Y. and Tzeng, G.H. (2000), “Using fuzzy integral for evaluating subjectively perceived travel costs in a traffic assignment model,” European Journal of Operational Research, 130(3), 653-664. Chen, T.Y., Wang, J.C. and Tzeng, G.H. (2000), “Identification of general fuzzy measures by genetic algorithm based on partial information,” IEEE Transactions on Systems, Man, and Cubernetics Part B: Cybernetics, 30B(4), 517-528. Dubois, D. and Prade, H. (1985), “A review of fuzzy set aggregation connectives,” Information Science, 36, 85-121. Grabisch, M., Nguyen, H.T. and Walker, E.A. (1995), Fundamentals of uncertainty calculi with applications to fuzzy inference, Dordrecht: Kluwer Academic Publish. Sugeno, M. (1974), Theory of Fuzzy Integral and Its Applications, unpublished doctoral dissertation, Tokyo Institute of Technology, Japan: Tokyo. Tzeng, G.H., Ou Yang, Y.P., Lin, C.T. and Chen, C.B. (2005a), “Hierarchical MADM with fuzzy integral for evaluating enterprise intranet web sites,” International Journal of Information Sciences, 169, 409-426. Tzeng, G.H., Chang, C.Y. and Lo, M.C. (2005b), “MADM Approach for Effecting Information Quality of Knowledge Management,” International Journal of Information Systems for Logistics and Management (IJISLM), 1 (1), 55-67. Yuan, B.J.C., Chang, C.Y. and Lo, M.C. (1998), “Strategies of Semiconductor Industry in Taiwan”, IEEE, IEMC 1998, 541-545. APPENDIX – FUZZY INTEGRAL The Choquet fuzzy integral of h(•) with fuzzy measure g (•) is defined as follows (Sugeno, 1974; see also: Chen and Tzeng, 2000; Chen et al., 2000, Tzeng et al., 2005a): (c) ∫ hdg = h( xn ) g ( H n ) + [h( xn −1 ) − h( xn )]g ( H n −1 ) + ... + [h( x1 ) − h( x2 )]g ( H1 ) = h( xn )[ g ( H n ) − g ( H n −1 )] + h( xn −1 )[ g ( H n −1 ) − g ( H n − 2 )] + ... + h( x1 ) g ( H1 ), (A.1) where H1 = {x1}, H 2 = {x1 , x2 },..., H n = {x1 , x2 ,..., xn } = X . In the above definition: 1) h is a measurable function from X to [0,1] and h( x1 ) ≥ h( x2 ) ≥ ... ≥ h( xn ). 2) Fuzzy density gi = g λ ({ xi } ) for any subset {x a1 , x a2 ,..., x ak } of X, is calculated from the equation: ak n ⎤ 1 ⎡ ak ak −1 g λ xa1 , xa2 ,..., xak = ∑ gi + λ ∑ ∑ gi g j + ... + λ g a1 g a2 ...g ak = ⎢∏ (1 + λ gi ) − 1⎥ λ ⎣ i = a1 i = a1 i = a1 j >i ⎦ (A.2) where {a1 , a2 ,..., ak } is any subset of {1, 2,..., k} in ascending order. 3) For −1 ≤ λ ≤ ∞ boundary condition g λ ({ x1 , x2 ,..., xn } ) = 1 leads to equation ({ }) λ + 1 = ∏1 + λ gi which can be solved for unique value of λ. n i =1