本論文旨在解決不確定需求下，接單生產環境中，單一種產品之BOM(Bill of Material)內各品項之生產規劃策略，目標值為極小化總成本。柯瓊琍(2001)論文已針對接單生產環境中，需求之時點和數量為已知下，發展出單一產品固定BOM中各品項之生產決策問題(MTS/MTO)之整數規劃模型。其問題中給定一個BOM，以一分割線(Partition Line；PTL)將整個BOM切割為二部分，PTL以下之品項以計劃式生產(MTS)；PTL以上之品項則以接單式生產(MTO)，目的為求得最小化成本下BOM內各項生產規劃方式及生產製造時間和數量。本研究將延伸其研究，主要為將顧客需求假設為不確定。
為表現需求不確定的問題，本論文首先發展一二階段隨機線性規劃模型(Two-Stage Stochastic Linear Programming Model)，並且以離散(discrete)、有限(finite)的機率分配來呈現需求之不確定性。模型中同時考慮MTO/MTS決策不同時的生產成本、存貨成本和缺貨成本，目的為找到BOM內各品項之最佳生產規劃方式，及MTS品項之最佳生產數量，期望能有效防止不確定需求對決策造成重大衝擊。
本研究用以求解二階段隨機線性規劃問題之解法為最常用以求解二階段隨機線性規劃之Benders Decomposition，並利用AMPL軟体來完成本研究之電腦計算求解。

參考文獻
黃世銘, “物流中心轉運量可擴充及顧客需求為隨機性假設下之多種貨品儲運分配系統設計”, 國防管理學院後勤管理研究碩士論文, 2000。
尹岳川, “在顧客需求為隨機性假設下多種貨品生產與儲運分配系統設計”, 國防管理學院後勤管理研究碩士論文, 2001。
柯瓊琍, “訂單生產環境下之BOM內各品項生產規劃之決策問題”, 國立中央大學工業管理研究碩士論文, 2001。
Benders, J.F. (1962), “Partitioning Procedures for Solving Mixed-Variable Programming Problems”, Numerische Mathematik 4, pp238-252
Birge, R. J. (1995), “Current Trends in Stochastic Programming Computation and Applications”, Department of Industrial and Operation Engineering, University of Michigan Ann Arbor, Michigan 48109-2117.
Birge, R.J. and Louveaux, F. (1997), “Introduction to Stochastic Programming”, Springer-Verlag NY.
Carøe, C.C. and Tind, J.(1997), “A Cutting-Plane Approach to Mixed 0-1 Stochastic Integer Programs”, European Journal of Operational Research 101, pp306-316.
Carøe, C.C. and Tind, J.(1998), “L-shaped Decomposition of Two-Stage Stochastic Programs with Integer Recourse”, Mathematical Programming 83, pp451-464.
Carøe, C.C. and Schultz, R.(1999), “Dual Decomposition in Stochastic Integer Programming”, Operation Research Letters 24, pp37-45.
Charnes, A., and Cooper, A.A. (1959), “Chance Constrained Programming”, Management Science 6, pp73-79.
Cheung, R.K.-M. and Powell, W.B.(1996), “Models and Algorithms for Distribution Problems with Uncertain Demands”, Transportation Science 30, pp43-59,
Dantzig, G. B. and Infanger, G. (1995), “A Probabilistic Lower Bound for Two-Stage Stochastic Programs”, Technical Report SOL 95-6, Department of Operations Research, Stanford University, Stanford, CA.
Fourer, R., Gay, D.M, and Kernighan, B. W. (1993), “A Modeling Language for Mathematical Programming”, Boyd and Fraser, Ferncroft Village, Danvers, MA.
Fragnière, E. , Gondzio, J. ,and Vial, Jean-Philippe(1998), “ A Planning Model with one Million Scenarios Solved on an Affordable Parallel Machine”, Logilab Technical Report 1998.11, Logilab, HEC, Section of Management Studies, University of Geneva, http://ecolu-info.unige.ch/~logilab/
Geoffrion, A. H.,(1970), “Elements of Large-Scale Mathematical Programming”, Management Science 16, pp652-685.
Geoffrion, A. H. and Graves G. W.(1974), “Multicommodity Distribution System Design by Benders Decompositioln”, Management Science 20, pp822-845.
Gassmann, H.I. (1996), “On the formulation of stochastic linear programs using algebraic modeling languages”, Annals of Operations Research 64, pp83-112.
Gupta, A. and Maranas C.D.(2000), “A Two-Stage Modeling and Solution Framework for Multisite Midterm Planning under Demand Uncertainty”, Ind. Eng. Chem. Res. 39, pp3799-3813.
Heragu, S. S., and Chen, Ja-Shen(1998), “Optimal Solution of cellular Manufacturing System Design: Benders’ Decomposition approach”, European Journal of Operation Research 107, pp175-192.
Infanger, G. (1994), “Planning under Uncertainty: Solving Large-Scale Stochastic Linear Programs”, Boyd and Fraser, Ferncroft Village, Danvers, MA.
Kall, P. and Wallace, S. W. (1994), “Stochastic Programming”, John Wiley &Sons, Chichester, England.
Laporte, G. and Louveaux, V. F. (1993), “The Integer L-shaped Method for Stochastic Integer Programs with Complete Recourse”, Operations Research Letters 13, PP133-142.
Prékopa, A. (1995), “Stochastic Programming”, Kluwer, Dordrecht, The Netherlands.
Schweitzer, E.(1994), “Multi-Stage Mathematical Programming under Uncertainty”, Research Thesis.
Subranhmanyam, S., Pekny, J.F., and Reklaitis, G.V.(1994), “Design of Batch Chemical Plants under Market Uncertainty”, Ind. Eng. Chem. Res. 33, pp2688-2701.
Valente, P., Mitra, G., Poojari, C., and Kyriakis, K. (2001), “Software tools of Stochastic Programming: A Stochastic Programming Integrated Environment (SPInE)”, Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH.
Van Slyke, R.M., and Wets, R.J.-B. (1996), “L-Shaped Linear Programs with Applications to Optimal Control and Stochastic Programming”, SIAM Journal on Applied Mathematics 17, pp638-663.
Wollmer, R.D.(1980), “Two Stage Linear Programming under Uncertainty with 0-1 Integer First Stage Variables”, Mathematical Programming 19, pp279-288.