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Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

Author

Listed:
  • Merve Bodur

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • Sanjeeb Dash

    (Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598)

  • Oktay Günlük

    (Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598)

  • James Luedtke

    (Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706)

Abstract

With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used to project the resulting improved relaxation, and (ii) project-and-cut, where integrality constraints are used to derive cuts directly in the Benders reformulation. For the case of split cuts, we demonstrate that although these approaches yield equivalent relaxations when considering a single split disjunction, cut-and-project yields stronger relaxations in general when using multiple split disjunctions. Computational results illustrate that the difference can be very large, and demonstrate that using split cuts within the cut-and-project framework can significantly improve the performance of Benders decomposition.

Suggested Citation

  • Merve Bodur & Sanjeeb Dash & Oktay Günlük & James Luedtke, 2017. "Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 77-91, February.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:1:p:77-91
    DOI: 10.1287/ijoc.2016.0717
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    References listed on IDEAS

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    1. Lewis Ntaimo, 2013. "Fenchel decomposition for stochastic mixed-integer programming," Journal of Global Optimization, Springer, vol. 55(1), pages 141-163, January.
    2. Daniel Bienstock & Oktay Günlük, 1996. "Capacitated Network Design---Polyhedral Structure and Computation," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 243-259, August.
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    Cited by:

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    13. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    14. Ksciuk, Jana & Kuhlemann, Stefan & Tierney, Kevin & Koberstein, Achim, 2023. "Uncertainty in maritime ship routing and scheduling: A Literature review," European Journal of Operational Research, Elsevier, vol. 308(2), pages 499-524.
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