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Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843
ntaimo{at}tamu.edu

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is presented. In particular, we derive valid inequalities that allow for scenario subproblems for SIP with random recourse but deterministic technology matrix and right-hand side vector to share cut coefficients. The valid inequalities are used to derive a disjunctive decomposition method whose derivation has been motivated by real-life stochastic server location problems with random recourse, which find many applications in operations research. Computational results with large-scale instances to demonstrate the potential of the method are reported.

Subject classifications: stochastic programming; integer programming; disjunctive programming.
History: Received November 2007; revision received July 2008; accepted September 2008.