Multicut Benders decomposition algorithm for process supply chain planning under uncertainty

• Published in: Annals of operations research Vol. 210; no. 1; pp. 191 - 211
• Main Authors: You, Fengqi, Grossmann, Ignacio E.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-11-2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Benders decomposition; Business and Management; Combinatorics; Computation; Decomposition; Decomposition (Mathematics); Feasibility; Iterative methods; Linear programming; Mathematical analysis; Mathematical models; Operations research; Operations Research/Decision Theory; Stochastic programming; Stochasticity; Supply chains; Theory of Computation; Uncertainty; Variables; United States; Supply chain; Planning; Benders decomposition; Stochastic programming
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-011-0974-4

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.