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Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

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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.

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Authors and Affiliations

  1. Argonne National Laboratory, Argonne, IL, 60439, USA

    Fengqi You

  2. Northwestern University, Evanston, IL, 60208, USA

    Fengqi You

  3. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Ignacio E. Grossmann

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  1. Fengqi You
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  2. Ignacio E. Grossmann
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Correspondence to Ignacio E. Grossmann.

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You, F., Grossmann, I.E. Multicut Benders decomposition algorithm for process supply chain planning under uncertainty. Ann Oper Res 210, 191–211 (2013). https://doi.org/10.1007/s10479-011-0974-4

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  • DOI: https://doi.org/10.1007/s10479-011-0974-4

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