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Schumann, a modeling framework for supply chain management under uncertainty. (English) Zbl 0933.90021

Summary: We present a modeling framework for the optimization of a Manufacturing, Assembly and Distribution (MAD) supply chain planning problem under uncertainty in product demand and component supplying cost and delivery time, mainly. The automotive sector has been chosen as the pilot area for this type of multiperiod multiproduct multilevel problem, but the approach has a far more reaching application. A deterministic treatment of the problem provides unsatisfactory results. We use a 2-stage scenario analysis based on a partial recourse approach, where MAD supply chain policy can be implemented for a given set of initial time periods, such that the solution for the other periods does not need to be anticipated and, then, it depends on the scenario to occur. In any case, it takes into consideration all the given scenarios. Very useful schemes are used for modeling balance equations and multiperiod linking constraints . A dual approach splitting variable scheme has been used for dealing with the implementable time periods related variables, via a redundant circular linking representation.

MSC:

90B30 Production models
90B50 Management decision making, including multiple objectives

Software:

CMIT; MSLiP
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Full Text: DOI

References:

[1] Afentakis, P.; Gavish, B.; Karamarkar, U., Computational efficient optimal solutions to the lot-sizing problem in multistage assembly systems, Management Science, 30, 222-239 (1984) · Zbl 0552.90045
[2] Alvarez, M.; Cuevas, C. M.; Escudero, L. F.; de la Fuente, J. L.; Garcı́a, C.; Prieto, F. J., Network planning under uncertainty with application to hydropower generation, TOP, 2, 25-28 (1994) · Zbl 0826.90075
[3] Baricelli, P.; Lucas, C.; Mitra, G., A model for strategic planning under uncertainty, TOP, 4, 361-384 (1996) · Zbl 0887.90091
[4] Beale, E. M.L., On minimizing a convex function subject to linear inequalities, Journal of Royal Statistics Society, 17b, 173-184 (1955) · Zbl 0068.13701
[5] Birge, J. R., Decomposition and partitioning methods for multistage linear programs, Operations Research, 33, 1089-1107 (1985)
[6] Birge, J. R.; Donohue, C. J.; Holmes, D. F.; Svintsistski, O. G., A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs, Mathematical Programming, 75, 327-352 (1996) · Zbl 0874.90142
[7] Birge, J.; Louveaux, F. V., A multicut algorithm for two-stage stochastic linear programs, European Journal of Operational Research, 34, 384-392 (1988) · Zbl 0647.90066
[8] Birge, J., Louveaux, F.V., 1997. Introduction to Stochastic Programming. Springer, Berlin; Birge, J., Louveaux, F.V., 1997. Introduction to Stochastic Programming. Springer, Berlin · Zbl 0892.90142
[9] Cheng, C.H., Miltenburg, J., submitted. A production planning problem where products have alternate routings and bills of material. European Journal of Operational Research; Cheng, C.H., Miltenburg, J., submitted. A production planning problem where products have alternate routings and bills of material. European Journal of Operational Research
[10] Cohen, M. A.; Lee, H. L., Resource deployment analysis of global manufacturing and distribution networks, Journal of Manufacturing and Operations Management, 2, 81-104 (1989)
[11] Cohen, M. A.; Moon, S., An integrated plant loading model with economics of scale and scope, European Journal of Operational Research, 50, 266-279 (1991) · Zbl 0721.90041
[12] Dantzig, G. B., Linear programming under uncertainty, Management Science, 1, 197-206 (1955) · Zbl 0995.90589
[13] Dantzig, G. B., Planning under uncertainty using parallel computing, Annals of Operations Research, 14, 1-17 (1985)
[14] Dembo, R. S., Scenario optimisation, Annals of Operations Research, 30, 63-80 (1991) · Zbl 0734.90061
[15] Dempster, M. A.H., On stochastic programming II: Dynamic problems under risk, Stochastics, 25, 15-42 (1988) · Zbl 0653.90054
[16] Dempster, M.A.H., Gassmann, H.I., 1990. Using the expected value of perfect information to simplify the decision tree. Abstracts 15th IFIP Conference on System Modeling and Optimization. IFIP, Zurich, pp. 301-303; Dempster, M.A.H., Gassmann, H.I., 1990. Using the expected value of perfect information to simplify the decision tree. Abstracts 15th IFIP Conference on System Modeling and Optimization. IFIP, Zurich, pp. 301-303
[17] Dempster, M.A.H., Thompson, R.T., to appear. EVPI-based importance sampling solution procedures for multistage stochastic linear programs on parallel MIMD Architectures. Annals of Operations Research; Dempster, M.A.H., Thompson, R.T., to appear. EVPI-based importance sampling solution procedures for multistage stochastic linear programs on parallel MIMD Architectures. Annals of Operations Research · Zbl 0937.90075
[18] Dzielinski, G. D.; Gomory, R., Optimal programming of lot sizes, inventory and lot size allocations, Management Science, 11, 874-890 (1965)
[19] Eppen, G. D.; Martin, R. K.; Schrage, L., A scenario approach to capacity planning, Operations Research, 37, 517-527 (1989)
[20] Escudero, L.F., 1994a. CMIT: a capacitated multi-level implosion tool for production planning. European Journal of Operational Research 76, 511-528; Escudero, L.F., 1994a. CMIT: a capacitated multi-level implosion tool for production planning. European Journal of Operational Research 76, 511-528 · Zbl 0810.90054
[21] Escudero, L.F., 1994b. Robust decision making as a decision making aid under uncertainty. In: Rios, S. (Ed.), Decision Theory and Decision Analysis. Kluwer Academic Publishers, Boston, MA, pp. 127-138; Escudero, L.F., 1994b. Robust decision making as a decision making aid under uncertainty. In: Rios, S. (Ed.), Decision Theory and Decision Analysis. Kluwer Academic Publishers, Boston, MA, pp. 127-138 · Zbl 0824.90093
[22] Escudero, L.F., Kamesam, P.V., 1993. MRP modeling via scenarios. In: Ciriani, T.A., Leachman, R.C. (Eds.), Optimisation in Industry. Wiley, New York, pp. 101-111; Escudero, L.F., Kamesam, P.V., 1993. MRP modeling via scenarios. In: Ciriani, T.A., Leachman, R.C. (Eds.), Optimisation in Industry. Wiley, New York, pp. 101-111
[23] Escudero, L. F.; Kamesam, P. V., On solving stochastic production planning problems via scenario modelling, TOP, 3, 69-96 (1995) · Zbl 0852.90084
[24] Escudero, L.F., Salmerón, J., 1998. 2-stage partial recourse for stochastic programming: A comparison of different modeling and algorithmic schemes. Working paper, IBERDROLA Ingenierı́a y Consultorı́a, Madrid, Spain; Escudero, L.F., Salmerón, J., 1998. 2-stage partial recourse for stochastic programming: A comparison of different modeling and algorithmic schemes. Working paper, IBERDROLA Ingenierı́a y Consultorı́a, Madrid, Spain
[25] Escudero, L.F., de la Fuente, J.L., Garcı́a, C., Prieto, F.J., to appear. A parallel computation approach for solving multistage stochastic network problems. Annals of Operations Research; Escudero, L.F., de la Fuente, J.L., Garcı́a, C., Prieto, F.J., to appear. A parallel computation approach for solving multistage stochastic network problems. Annals of Operations Research · Zbl 0937.90111
[26] Escudero, L. F.; Kamesam, P. V.; King, A. J.; Wets, R. J.-B., Production planning via scenario modelling, Annals of Operations Research, 43, 311-335 (1993) · Zbl 0784.90033
[27] Florian, M.; Klein, M., Deterministic production planning with concave costs and capacity constraints, Management Science, 18, 12-20 (1971) · Zbl 0273.90023
[28] Gassmann, H. I., MSLiP: A computer code for the multistage stochastic linear programming problem, Mathematical Programming, 4, 407-423 (1990) · Zbl 0701.90070
[29] Goyal, S. K.; Gunasekaran, A., Multi-stage production-inventory systems, European Journal of Operational Research, 46, 1-20 (1990) · Zbl 0702.90035
[30] Graves, S. C.; Fine, C. H., A tactical planning model for manufacturing subcomponents of mainframe computers, Journal of Manufacturing and Operations Management, 2, 4-34 (1988)
[31] Higle, J.L., Sen, S., 1996. Stochastic Decomposition. A Statistical Method for Large-Scale Stochastic Linear Programming. Kluwer Academic Publishers, Boston, MA; Higle, J.L., Sen, S., 1996. Stochastic Decomposition. A Statistical Method for Large-Scale Stochastic Linear Programming. Kluwer Academic Publishers, Boston, MA · Zbl 0874.90145
[32] Infanger, G., 1994. Planning under Uncertainty, Solving Stochastic Linear Programs. Boyel & Fraser; Infanger, G., 1994. Planning under Uncertainty, Solving Stochastic Linear Programs. Boyel & Fraser · Zbl 0867.90086
[33] Kall, P., Wallace, S., 1994. Stochastic Programming. Wiley, New York; Kall, P., Wallace, S., 1994. Stochastic Programming. Wiley, New York
[34] Karmarkar, U. S., Lot sizes, lead times and in process inventories, Management Sciences, 33, 409-423 (1987) · Zbl 0612.90068
[35] Karmarkar, U. S., Capacity loading and release planning with work in progress and lead times, Journal of Manufacturing and Operations Management, 2, 105-123 (1989)
[36] Kekre, S., Kekre, S., 1985. Work in progress considerations in job shop capacity planning. Working paper GSIA, Carnegie Mellon University, Pittsburgh, PA; Kekre, S., Kekre, S., 1985. Work in progress considerations in job shop capacity planning. Working paper GSIA, Carnegie Mellon University, Pittsburgh, PA
[37] Lasdon, L. S.; Terjung, R. C., An efficient algorithm for multi-echelon scheduling, Operations Research, 19, 946-969 (1971) · Zbl 0224.90039
[38] Mulvey, J. M.; Vanderbei, R. J.; Zenios, S. A., Robust optimisation of large-scale systems: General modelling framework and computations, Operations Research, 43, 244-281 (1995)
[39] Mulvey, J. M.; Vladimirou, H., Solving multistage stochastic networks: An application of scenario aggregation, Networks, 21, 619-643 (1991) · Zbl 0743.90053
[40] Mulvey, J. M.; Ruszczynski, A., A diagonal quadratic approximation method for large-scale linear programs, Operations Research Letters, 12, 205-221 (1992) · Zbl 0767.90047
[41] Rockafellar, R. T.; Wets, R. J.-B., Scenario and policy aggregation in optimisation under uncertainty, Mathematics of Operations Research, 16, 119-147 (1991) · Zbl 0729.90067
[42] Ruszczynski, A., Parallel decomposition of multistage stochastic programs, Mathematical Programming, 58, 201-208 (1993) · Zbl 0777.90036
[43] Shapiro, J.F., 1993. Mathematical programming models and methods for production planning and scheduling. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, E. (Eds.), Logistics of Production and Inventory. North-Holland, Amsterdam, pp. 371-443; Shapiro, J.F., 1993. Mathematical programming models and methods for production planning and scheduling. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, E. (Eds.), Logistics of Production and Inventory. North-Holland, Amsterdam, pp. 371-443
[44] Van Slyke, R.; Wets, R. J.-B., L-shaped linear programs with applications to optimal control and stochastic programming, SIAM Journal on Applied Mathematics, 17, 638-663 (1969) · Zbl 0197.45602
[45] Vladimirou, H., to appear. Computational assessment of distributed decomposition methods for stochastic linear programs. European Journal of Operational Research; Vladimirou, H., to appear. Computational assessment of distributed decomposition methods for stochastic linear programs. European Journal of Operational Research · Zbl 0932.90028
[46] Vladimirou, H.; Zenios, S. A., Stochastic linear programs with restricted recourse, European Journal of Operational Research, 101, 177-192 (1997) · Zbl 0918.90110
[47] Wets, R.J.-B., 1988. Large-scale linear programming techniques. In: Ermoliev, Y., Wets, R.J.-B. (Eds.), Numerical Techniques for Stochastic Optimization. Springer, Berlin, pp. 65-93; Wets, R.J.-B., 1988. Large-scale linear programming techniques. In: Ermoliev, Y., Wets, R.J.-B. (Eds.), Numerical Techniques for Stochastic Optimization. Springer, Berlin, pp. 65-93 · Zbl 0676.90043
[48] Wets, R.J.-B., 1989. The aggregation principle in scenario analysis and stochastic optimisation. In: Wallace, S.W. (Ed.), Algorithms and Model Formulations in Mathematical Programming. Springer, Berlin, pp. 92-113; Wets, R.J.-B., 1989. The aggregation principle in scenario analysis and stochastic optimisation. In: Wallace, S.W. (Ed.), Algorithms and Model Formulations in Mathematical Programming. Springer, Berlin, pp. 92-113
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