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Finitely Convergent Decomposition Algorithms for Two-Stage Stochastic Pure Integer Programs

Minjiao Zhang (zhang.769***at***osu.edu)
Simge Küçükyavuz (kucukyavuz.2***at***osu.edu)

Abstract: We study a class of two-stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters. Based on Benders' method, we propose a decomposition algorithm that utilizes Gomory cuts in both stages. The Gomory cuts for the second-stage scenario subproblems are parameterized by the first-stage decision variables, i.e., they are valid for any feasible first-stage solutions. In addition, we propose an alternative implementation that incorporates Benders' decomposition into a branch-and-cut process in the first stage. We prove the finite convergence of the proposed algorithms. We also report our preliminary computations with a rudimentary implementation of our algorithms to illustrate their effectiveness.

Keywords: Two-stage stochastic pure integer programs, Gomory cuts, Benders' decomposition

Category 1: Integer Programming

Category 2: Stochastic Programming

Citation: Technical Report, Department of Integrated Systems Engineering, The Ohio State University

Download: [PDF]

Entry Submitted: 06/27/2013
Entry Accepted: 06/28/2013
Entry Last Modified: 05/07/2014

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