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Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

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  • Fengqi You
  • Ignacio Grossmann

Abstract

In this paper, we present a multicut version of the Benders decomposition method for solving two-stage stochastic linear programming problems, including stochastic mixed-integer programs with only continuous recourse (two-stage) variables. The main idea is to add one cut per realization of uncertainty to the master problem in each iteration, that is, as many Benders cuts as the number of scenarios added to the master problem in each iteration. Two examples are presented to illustrate the application of the proposed algorithm. One involves production-transportation planning under demand uncertainty, and the other one involves multiperiod planning of global, multiproduct chemical supply chains under demand and freight rate uncertainty. Computational studies show that while both the standard and the multicut versions of the Benders decomposition method can solve large-scale stochastic programming problems with reasonable computational effort, significant savings in CPU time can be achieved by using the proposed multicut algorithm. Copyright Springer Science+Business Media, LLC 2013

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  • Fengqi You & Ignacio Grossmann, 2013. "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Annals of Operations Research, Springer, vol. 210(1), pages 191-211, November.
    • Handle: RePEc:spr:annopr:v:210:y:2013:i:1:p:191-211:10.1007/s10479-011-0974-4
    DOI: 10.1007/s10479-011-0974-4
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    1. Lewis Ntaimo, 2010. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse," Operations Research, INFORMS, vol. 58(1), pages 229-243, February.
    2. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
    3. L. Escudero & A. Garín & M. Merino & G. Pérez, 2007. "A two-stage stochastic integer programming approach as a mixture of Branch-and-Fix Coordination and Benders Decomposition schemes," Annals of Operations Research, Springer, vol. 152(1), pages 395-420, July.
    4. Jesús Latorre & Santiago Cerisola & Andrés Ramos & Rafael Palacios, 2009. "Analysis of stochastic problem decomposition algorithms in computational grids," Annals of Operations Research, Springer, vol. 166(1), pages 355-373, February.
    5. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    6. Trukhanov, Svyatoslav & Ntaimo, Lewis & Schaefer, Andrew, 2010. "Adaptive multicut aggregation for two-stage stochastic linear programs with recourse," European Journal of Operational Research, Elsevier, vol. 206(2), pages 395-406, October.
    7. T W Archibald & C S Buchanan & K I M McKinnon & L C Thomas, 1999. "Nested Benders decomposition and dynamic programming for reservoir optimisation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(5), pages 468-479, May.
    8. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
    9. Emmanuel Fragnière & Jacek Gondzio & Jean-Philippe Vial, 2000. "Building and Solving Large-Scale Stochastic Programs on an Affordable Distributed Computing System," Annals of Operations Research, Springer, vol. 99(1), pages 167-187, December.
    10. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    11. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
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    8. Amorim, Pedro & Curcio, Eduardo & Almada-Lobo, Bernardo & Barbosa-Póvoa, Ana P.F.D. & Grossmann, Ignacio E., 2016. "Supplier selection in the processed food industry under uncertainty," European Journal of Operational Research, Elsevier, vol. 252(3), pages 801-814.
    9. Blanchot, Xavier & Clautiaux, François & Detienne, Boris & Froger, Aurélien & Ruiz, Manuel, 2023. "The Benders by batch algorithm: Design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 202-216.
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