半導體產業由於設備成本高昂，因此產能的充分利用是半導體晶圓廠相當重要的議題；另一方面，在客戶導向的經營策略下，滿足客戶的需求亦是晶圓代工廠的主要目標之一。客戶需求的滿足對於產能利用率以及客戶滿意度均有相當重要的影響，因此，本研究探討如何規劃產品的分配與產能的調度以達到最佳的需求滿足及維持產能利用率。
由於半導體製程相當精密，產品需經過光罩製作、試產及驗證的流程後方能進行量產，需花費較長的前置時間及光罩成本，¬而且光罩無法在不同廠間互用。此些特性造成產品無法隨意分配至不同廠進行生產，故新產品的分配對未來各廠之需求影響極大。
本研究考慮新產品投片分配之影響以建構半導體業之需求滿足模式，並以成本最小化為目標，從產品分配決策對各廠生產產品能力之影響以及廠間與廠內之產能備援機制之採用來達成需求的滿足。本研究建構需求滿足之確定性模式及兩階段隨機規劃模式以在考慮需求不確定性的情況下進行決策。此外，本研究以一數值案例驗證隨機規劃模式在需求不確定之情況下之表現，其結果顯示隨機規劃模式在需求情境改變下較確定性模式表現更佳，能達到較低之成本來滿足顧客之需求。另外，本研究亦對不同需求水準下所進行之產品分配以及產能備援決策之差異進行討論。

In the semiconductor industry, the capital expenditure of capacity investment is so high that the manufacturers tend to keep their fabs highly utilized. In addition, customer satisfaction has been recognized as an important performance measure especially for foundry companies. Demand fulfillment has a great influence on both capacity utilization and customer satisfaction and therefore has become a critical job.
The semiconductor manufacturing process is very complex that each product is required to go through the process of mask creation, pilot run, and qualification so that it could be volume produced. This process will take a long lead time and high mask costs. Furthermore, the masks are not interchangeable between fabs. The above characteristics limit the production capability of fabs and products could not be arbitrarily assigned to fabs for production. Therefore, the NTO allocation affects the future demand of fabs very much.
This research aims to develop a demand fulfillment model considering NTO allocation problem. The decisions of product allocation and capacity backup are considered to construct the model. The problem is formulated as both deterministic model and stochastic model to incorporate demand uncertainty for decision making. Finally, a numerical study is conducted to evaluate the performance of the stochastic model and results show that the stochastic model can achieve a lower cost as the demand scenario changes. Also, discussions about the differences of decisions under different level of demand volume are provided.

Ahmed, S. (2002), “Semiconductor tool planning via multi-stage stochastic programming,” in: Proceedings of the 2002 international conference on modeling and analysis of semiconductor manufacturing, USA: Tempe, Arizona, pp. 153-157.
Ahmed, S., A. J. King, and G. Parija (2003), “A multi-stage stochastic integer programming approach for capacity expansion under uncertainty,” Journal of Global Optimization, Vol. 26, No. 1, pp. 3-24.
Ahmed, S. and N. V. Sahinidis (2003), “An approximation scheme for stochastic integer programs arising in capacity expansion,” Operations Research, Vol. 51, No. 3, pp. 461–471.
Ahmed, S. and R. Garcia (2004), “Dynamic capacity acquisition and assignment under uncertainty,” Annals of Operations Research, Vol. 124, No. 1, pp. 267-283.
Barahona, F., Bermon, S., Gunluk, O. and Hood, S. (2001), Robust capacity planning in semiconductor manufacturing, IBM (Research Report RC22196).
Bermon, S. and S. Hood (1999), “Capacity optimization planning system (CAPS),” Interfaces, Vol. 29, No. 5, pp. 31–50.
Bilgin, S. and M. Azizoglu (2009), “Operation assignment and capacity allocation problem in automated manufacturing systems,” Computers & Industrial Engineering, Vol. 56, No. 2, pp. 662-676.
Birge, J. R. (1982), “The value of the stochastic solution in stochastic linear programs with fixed recourse,” Mathematical Programming, Vol. 24, No. 1, pp. 314-325.
Chen, Z. L., S. Li, D. Tirupati (2002), “A scenario-based stochastic programming approach for technology and capacity planning,” Computers & Operations Research, Vol. 29, No. 7, pp. 781-806.
Chou, Y. C., C. T. Cheng, F. C. Yang, Y. Y. Liang (2007), “Evaluating alternative capacity strategies in semiconductor manufacturing under uncertain demand and price scenarios,” International Journal of Production Economics, Vol. 105, No. 2, pp. 591–606.
Chou, Y. C. and R. C. You (2001), “A resource portfolio planning methodology for semiconductor wafer manufacturing,” International Journal of Advanced Manufacturing Technology, Vol. 18, No. 1, pp. 12–19.
Christie, R. M. E. and S. D. Wu (2002), “Semiconductor capacity planning: stochastic modeling and computational studies,” IIE Transactions, Vol. 34, No. 2, pp. 131-143.
Chung, S. H., C. Y. Huang, A. H. I. Lee (2006), ”Capacity allocation model for photolithography workstation with the constraints of process window and machine dedication,” Production Planning & Control, Vol. 17, No. 7, pp. 678-688.
Diwekar, U. (2008), Introduction to Applied Optimization, Second Edition, Kluwer Academic Publishers, Netherlands.
Fleischmann, B., S. Ferber, P. Henrich (2006), “Strategic planning of BMW’s global production network,” Interfaces, Vol. 36, No. 3, pp. 194-208.
Geng, N., Z. Jiang, F. Chen (2009), “Stochastic programming based capacity planning for semiconductor wafer fab with uncertain demand and capacity,” European Journal of Operational Research, Vol. 198, No. 3, pp. 899–908.
Hood, S. J., S. Bermon, and F. Barahona (2003), “Capacity planning under demand uncertainty for semiconductor manufacturing,” IEEE Transactions on Semiconductor Manufacturing, Vol. 16, No. 2, pp. 273-280.
Huang, K. and S. Ahmed (2005), The value of multi-stage stochastic programming in capacity planning under uncertainty, Technical Report, School of Industrial & Systems Engineering, Georgia Tech.
Inman, R. R., D. J. A. Gonsalvez (2001), “A mass production product-to-plant allocation problem,” Computers & Industrial Engineering, Vol. 39, No. 3, pp. 255-271.
Jordan, W. C., S. C. Graves (1995), “Principles ion the benefits of manufacturing process flexibility,” Management Science, Vol. 41, No. 4, pp. 577-594.
Kang, K. H. and Y. H. Lee (2007), “Make-to-order scheduling in foundry semiconductor fabrication,” International Journal of Production Research, Vol. 45, No. 3, pp. 615-630.
Karabuk, S. (2001), Coordinating capacity decisions for the supply chain in high-tech industry, Dissertation (PhD), Lehigh University.
Karabuk, S. and S. D. Wu (2003), “Coordinating strategic capacity planning in the semiconductor industry,” Operations Research, Vol. 51, No. 6, pp. 839-849.
Kauder, S., H. Meyr (2009), “Strategic network planning for an international automotive manufacturer,” OR Spectrum, Vol. 31, No. 3, pp. 507-532.
Leachman, R. C. and T. F. Carmon (1992), “On capacity modeling for production planning with alternative machines,” IIE Transactions, Vol. 24, No. 4, pp. 62–72.
Lin, Y. S., Y. H. Chang, Y. C. Chou (2005), “Application of stochastic programming to tool portfolio planning in semiconductor manufacturing,” Journal of Management & Systems, Vol. 12, No. 4, pp. 1-155.
Mollaghsemi, M. and G. W. Evans (1994), “Multicriteria design of manufacturing systems through simulation optimization,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 24, No. 9, pp. 1407–1411.
Mulvey, J. M., R. J. Vanderbei, and S. A. Zenios (1995), “Robust optimization of large-scale systems,” Operations Research, Vol. 43, No. 2, pp. 264-281.
Ozturk, O., M. B. Coburn and S. Kitterman (2003), “”Conceptualization, design and implementation of a static capacity model,” Simulation Conference, pp. 1373–1376.
Rupp, T. M. and M. Ristic (2000), “Fine planning for supply chains in semiconductor manufacture,” Journal of Materials Processing Technology, Vol. 107, No. 1, pp. 390-397
Swaminathan, J. M. (2000), “Tool capacity planning for semiconductor fabrication facilities under demand uncertainty,” European Journal of Operational Research, Vol. 120, No. 3, pp. 545-558.
Swaminathan, J. M. (2002), “Tool procurement planning for wafer fabrication facilities: a scenario-based approach,” IIE Transactions, Vol. 34, No. 2, pp. 144-155.
Wang, K. J., S. M. Wang, and S. J. Yang (2007), “A resource portfolio model for equipment investment and allocation of semiconductor testing industry,” European Journal of Operational Research, Vol. 179, No. 2, pp. 390-403
Witte, J. D. (1996), “Using static capacity modeling techniques in semiconductor industry,” IEEE/SEMI Advanced Semiconductor Manufacturing Conference and Workshop, pp. 31-35
Wu, J. Z. and C. F. Chien (2008), “Modeling strategic semiconductor assembly outsourcing decisions based on empirical settings,” OR Spectrum, Vol. 30, No. 3, pp. 401-430.
Wu, M. C., Y. Hsiung, and H. M. Hsu (2005), “A tool planning approach considering cycle time constraints and demand uncertainty,” International Journal of Advanced Manufacturing Technology, Vol. 26, No. 5, pp. 565–571.
Wu, S. D., M. Erkoc, and S. Karabuk (2005), “Managing Capacity in the High-Tech Industry: A Review of Literature,” The Engineering Economist, Vol. 50, No. 2, pp. 125-158.
Zhang, R. Q. (2007), “Research on capacity planning under stochastic production and uncertain demand,” Systems Engineering - Theory & Practice, Vol. 27, No. 1, pp. 51-59.