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A binary decision diagram based algorithm for solving a class of binary two-stage stochastic programs

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Abstract

We consider a special class of two-stage stochastic integer programming problems with binary variables appearing in both stages. The class of problems we consider constrains the second-stage variables to belong to the intersection of sets corresponding to first-stage binary variables that equal one. Our approach seeks to uncover strong dual formulations to the second-stage problems by transforming them into dynamic programming (DP) problems parameterized by first-stage variables. We demonstrate how these DPs can be formed by use of binary decision diagrams, which then yield traditional Benders inequalities that can be strengthened based on observations regarding the structure of the underlying DPs. We demonstrate the efficacy of our approach on a set of stochastic traveling salesman problems.

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Acknowledgements

The authors are grateful for the remarks of two anonymous referees and a guest editor, whose comments led to a greatly improved version of this paper. Dr. Smith gratefully acknowledges the support of the Air Force Office of Scientific Research under Grant FA9550-12-1-0353 and the Office of Naval Research under Grants N00014-13-1-0036 and N00014-17-1-2421.

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Authors and Affiliations

  1. Department of Industrial Engineering, Clemson University, 278 Freeman Hall, Clemson, SC, 29634, USA

    Leonardo Lozano

  2. Department of Industrial Engineering, Clemson University, 100 Freeman Hall, Clemson, SC, 29634, USA

    J. Cole Smith

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  1. Leonardo Lozano
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Correspondence to J. Cole Smith.

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Lozano, L., Smith, J.C. A binary decision diagram based algorithm for solving a class of binary two-stage stochastic programs. Math. Program. 191, 381–404 (2022). https://doi.org/10.1007/s10107-018-1315-z

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  • DOI: https://doi.org/10.1007/s10107-018-1315-z

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