Abstract
In this paper, a transportation problem comprising stochastic demands, fixed handling costs at the origins, and fixed costs associated with the links is addressed. It is assumed that uncertainty is adequately captured via a finite set of scenarios. The problem is formulated as a two-stage stochastic program. The goal is to minimize the total cost associated with the selected links plus the expected transportation and fixed handling costs. A prototype problem is initially presented which is then progressively extended to accommodate capacities at the origins and multiple commodities. The results of an extensive set of computational tests are reported and discussed.
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References
Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice Hall, London
Barbarosoǧlu G, Arda Y (2004) A two-stage stochastic programming framework for transportation planning in disaster response. J Oper Res Soc 55:43–53
Birge JR (1982) The value of the stochastic solution in stochastic linear programs with fixed recourse. Math Prog 24:314–325
Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, London
Escudero LF (2009) On a mixture of the fix-and-relax coordination and lagrangian substitution schemes for multistage stochastic mixed integer programming. TOP 17:5–29
Escudero LF, Garín A, Merino M, Prezé G (2007) The value of the stochastic solution in multistage problems. TOP 15:48–64
Escudero LF, Garín MA, Pérez G, Unzueta A (2012) Lagrangian decomposition for large-scale two-stage stochastic mixed 0–1 problems. TOP 20:347–374
França PM, Luna HPL (1982) Solving stochastic transportation–location problems by generalized Benders decomposition. Transp Sci 16(2):113–126
Grieco S, Semeraro U, Tolio T (2001) A review of different approaches to the fms loading problem. Int J Flexible Manuf Syst 13(4):361–384
Holmberg K (1995) Efficient decomposition and linearization methods for the stochastic transportation problem. Comput Optim Appl 4:293–316
Holmberg K, Jörnsten KO (1984) Cross decomposition applied to the stochastic transportation problem. Eur J Oper Res 17(3)
Holmberg K, Tuy H (1999) A production–transportation problem with stochastic demand and concave production costs. Math Prog 85:157–179
LeBlanc LJ (1977) A heuristic approach for large scale discrete stochastic transportation–location problems. Computers Math Appl 3:87–94
Li ACY, Nozick L, Xu N, Davidson R (2012) Shelter location and transportation planning under hurricane conditions. Transp Res Part E: Logistics Transp Rev 48:715–729
Lium A-G, Crainic TG, Wallace SW (2009) A study of demand stochasticity in service network design. Transp Sci 43:144–157
Max Shen Z-J, Coullard C, Daskin MS (2003) Joint location–inventory model. Transp Sci 37(1):40–55
Qi L (1985) Forest iteration method for stochastic transportation problem. Math Prog Study 25:142–163
Thapalia BK, Crainic TG, Kaut M, Wallace SW (2012a) Single-commodity network design with random edge capacities. Eur J Oper Res 220:394–403
Thapalia BK, Crainic TG, Kaut M, Wallace SW (2012b) Single-commodity stochastic network design with multiple sources and sinks. INFOR 49:193–211
Tsai M-T, Saphores J-D, Regan A (2011) Valuation of freight transportation contracts under uncertainty. Transp Res Part E: Logistics Transp Rev 47:920–932
Williams AC (1963) A stochastic transportation problem. Oper Res 11(5):759–770
Xu N, Nozick L (2009) Modeling supplier selection and the use of option contracts for global supply chain design. Computers Oper Res 36:2786–2800
Acknowledgments
This research has been partially supported by projects FQM-5849 (Junta de Andalucía\(\backslash \)FEDER) and MTM2010-19576-C02-01 (MICINN, Spain) and by the Portuguese Science Foundation—Centro de Investigação Operacional. The authors would like to express their gratitude to the anonymous referees for the constructive comments and suggestions given, which helped to improve the paper.
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Hinojosa, Y., Puerto, J. & Saldanha-da-Gama, F. A two-stage stochastic transportation problem with fixed handling costs and a priori selection of the distribution channels. TOP 22, 1123–1147 (2014). https://doi.org/10.1007/s11750-014-0321-4
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DOI: https://doi.org/10.1007/s11750-014-0321-4