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A stochastic programming approach for supply chain network design under uncertainty. (English) Zbl 1075.90010
Summary: This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the sample average approximation (SAA) scheme, with an accelerated Benders decomposition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.

90B10 Deterministic network models in operations research
90C15 Stochastic programming
Full Text: DOI
[1] Aikens, C.H., Facility location models for distribution planning, European journal of operational research, 22, 3, 263-279, (1985) · Zbl 0583.90022
[2] Alonso-Ayuso, A.; Escudero, L.F.; Garin, A.; Ortuno, M.T.; Perez, G., An approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming, Journal of global optimization, 26, 97-124, (2003) · Zbl 1116.90383
[3] Benders, J.F., Partitioning procedures for solving mixed variables programming problems, Numersiche Mathematik, 4, 238-252, (1962) · Zbl 0109.38302
[4] Birge, J.R.; Louveaux, F., Introduction to stochastic programming, (1997), Springer New York · Zbl 0892.90142
[5] Birge, J.R.; Louveaux, F.V., A multicut algorithm for two-stage stochastic linear programs, European journal of operational research, 34, 3, 384-392, (1988) · Zbl 0647.90066
[6] Cheung, R.K.-M.; Powell, W.B., Models and algorithms for distribution problems with uncertain demands, Transportation science, 30, 43-59, (1996) · Zbl 0851.90030
[7] Dogan, K.; Goetschalckx, M., A primal decomposition method for the integrated design of multi-period production – distribution systems, IIE transactions, 31, 1027-1036, (1999)
[8] Geoffrion, A.M.; Graves, G.W., Multi-commodity distribution system design by benders decomposition, Management science, 20, 822-844, (1974) · Zbl 0304.90122
[9] Geoffrion, A.M.; Powers, R.F., Twenty years of strategic distribution system design: an evolutionary perspective, Interfaces, 25, 105-128, (1995)
[10] Gutierrez, G.J.; Kouvelis, P.; Kurawala, A.A., A robustness approach to uncapacitated network design problems, European journal of operations research, 94, 362-376, (1996) · Zbl 0953.90503
[11] Hamming, R.W., Error detecting and error correcting codes, Bell system tech journal, 9, 147-160, (1950) · Zbl 1402.94084
[12] M. Hicks, When the chain snaps, eWeek–Enterprise News & Reviews. Available from <http://www.eweek.com>, 2002
[13] Hiriart-Urruty, J.-B.; Lemaréchal, C., Convex analysis and minimization algorithms II, (1996), Springer-Verlag Berlin
[14] ILOG Inc, CPLEX 7.0 User’s Manual, ILOG CPLEX Division, Incline Village, NV, 2000
[15] Kamath, K.R.; Pakkala, T.P.M., A Bayesian approach to a dynamic inventory model under an unknown demand distribution, Computers & operations research, 29, 403-422, (2002) · Zbl 1005.90006
[16] Kleywegt, A.J.; Shapiro, A.; Homem-De-Mello, T., The sample average approximation method for stochastic discrete optimization, SIAM journal of optimization, 12, 479-502, (2001) · Zbl 0991.90090
[17] Van Landeghem, H.; Vanmaele, H., Robust planning: A new paradigm for demand chain planning, Journal of operations management, 20, 769-783, (2002)
[18] J.T. Linderoth, A. Shapiro, S.J. Wright, The empirical behavior of sampling methods for stochastic programming, Annals of Operations Research (forthcoming) · Zbl 1122.90391
[19] Linderoth, J.T.; Wright, S.J., Implementing a decomposition algorithm for stochastic programming on a computational grid, Computational optimization and applications, 24, 207-250, (2003) · Zbl 1094.90026
[20] Magnanti, T.L.; Wong, R.T., Accelerating benders decomposition: algorithmic enhancement and model selection criteria, Operations research, 29, 464-484, (1981) · Zbl 0455.90064
[21] Mak, W.K.; Morton, D.P.; Wood, R.K., Monte Carlo bounding techniques for determining solution quality in stochastic programs, Operations research letters, 24, 47-56, (1999) · Zbl 0956.90022
[22] MirHassani, S.A.; Lucas, C.; Mitra, G.; Messina, E.; Poojari, C.A., Computational solution of capacity planning models under uncertainty, Parallel computing, 26, 511-538, (2000) · Zbl 0942.90030
[23] Norkin, V.I.; Pflug, G.Ch.; Ruszczyński, A., A branch and bound method for stochastic global optimization, Mathematical programming, 83, 425-450, (1998) · Zbl 0920.90111
[24] Norkin, V.I.; Ermoliev, Y.M.; Ruszczyński, A., On optimal allocation of indivisibles under uncertainty, Operations research, 46, 381-395, (1998) · Zbl 0987.90064
[25] Owen, S.H.; Daskin, M.S., Strategic facility location: A review, European journal of operational research, 111, 423-447, (1998) · Zbl 0938.90048
[26] Ruszczyński, A., A regularized decomposition method for minimizing a sum of polyhedral functions, Mathematical programming, 35, 309-333, (1986) · Zbl 0599.90103
[27] T. Santoso, A comprehensive model and efficient solution algorithm for the design of global supply chains under uncertainty, Ph.D. Thesis, School of Industrial & Systems Engineering, Georgia Institute of Technology, 2002
[28] Shapiro, A.; Homem de Mello, T., A simulation-based approach to stochastic programming with recourse, Mathematical programming, 81, 301-325, (1998) · Zbl 0919.90120
[29] Tsiakis, P.; Shah, N.; Pantelides, C.C., Design of multi-echelon supply chain networks under demand uncertainty, Industrial & engineering chemistry research, 40, 3585-3604, (2001)
[30] 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
[31] Verweij, B.; Ahmed, S.; Kleywegt, A.J.; Nemhauser, G.; Shapiro, A., The sample average approximation method applied to stochastic routing problems: A computational study, Computational optimization and applications, 24, 289-333, (2003) · Zbl 1094.90029
[32] Vidal, C.; Goetschalckx, M., Strategic production – distribution models: A critical review with emphasis on global supply chain models, European journal of operational research, 98, 1-18, (1997) · Zbl 0922.90062
[33] Vidal, C.; Goetschalckx, M., A global supply chain model with transfer pricing and transportation cost allocation, European journal of operational research, 129, 134-158, (2001) · Zbl 0990.90008
[34] Yu, C.-S.; Li, H.-L., A robust optimization model for stochastic logistic problems, International journal of production economics, 64, 385-397, (2000)
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