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Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework

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  • Maher, Stephen J.

Abstract

Benders’ decomposition is a popular mathematical and constraint programming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure in mathematical and constraint programs, the use of Benders’ decomposition typically requires significant implementation effort to achieve an effective solution algorithm. Traditionally, Benders’ decomposition has been viewed as a problem specific algorithm, which has limited the development of general purpose algorithms and software solutions. This paper presents a general purpose Benders’ decomposition algorithm that is capable of handling many classes of mathematical and constraint programs and provides extensive flexibility in the implementation and use of this algorithm. A branch-and-cut approach for Benders’ decomposition has been implemented within the constraint integer programming solver SCIP using a plugin-based design to allow for a wide variety of extensions and customisations to the algorithm. The effectiveness of the Benders’ decomposition algorithm and available enhancement techniques is assessed in a comprehensive computational study.

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  • 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.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:2:p:479-498
    DOI: 10.1016/j.ejor.2020.08.037
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    1. Jean-François Cordeau & Goran Stojković & François Soumis & Jacques Desrosiers, 2001. "Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling," Transportation Science, INFORMS, vol. 35(4), pages 375-388, November.
    2. Álvarez-Miranda, Eduardo & Fernández, Elena & Ljubić, Ivana, 2015. "The recoverable robust facility location problem," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 93-120.
    3. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
    4. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    5. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    6. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    7. 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.
    8. Gustavo Angulo & Shabbir Ahmed & Santanu S. Dey, 2016. "Improving the Integer L-Shaped Method," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 483-499, August.
    9. Matteo Fischetti & Ivana Ljubić & Markus Sinnl, 2017. "Redesigning Benders Decomposition for Large-Scale Facility Location," Management Science, INFORMS, vol. 63(7), pages 2146-2162, July.
    10. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    11. K. A. Ariyawansa & Andrew J. Felt, 2004. "On a New Collection of Stochastic Linear Programming Test Problems," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 291-299, August.
    12. Y. Xu & T. K. Ralphs & L. Ladányi & M. J. Saltzman, 2009. "Computational Experience with a Software Framework for Parallel Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 383-397, August.
    13. Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    14. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    15. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
    16. Joe Naoum-Sawaya & Samir Elhedhli, 2013. "An interior-point Benders based branch-and-cut algorithm for mixed integer programs," Annals of Operations Research, Springer, vol. 210(1), pages 33-55, November.
    17. Gary Froyland & Stephen J. Maher & Cheng-Lung Wu, 2014. "The Recoverable Robust Tail Assignment Problem," Transportation Science, INFORMS, vol. 48(3), pages 351-372, August.
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