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Benders-type branch-and-cut algorithms for capacitated facility location with single-sourcing

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  • Weninger, Dieter
  • Wolsey, Laurence A.

Abstract

We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0–1 variables xj indicating whether faclility j is used or not and yij variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, the remaining problem is a transportation problem with single-sourcing. This structure suggest the use of a Benders’ type decomposition algorithm. Here we present three possible variants. Applied to CFLP-SS they are compared computationally with a commercial solver (CPLEX) on the original formulation, a CPLEX version of Benders and a recent cut-and-solve approach developed specifically for CFLP-SS. Our results show that for CFLP-SS, when the percentage of clients requiring single-sourcing is less equal than 25%, the Benders’ variants achieve speedups of between 1.2 and 3.7.

Suggested Citation

  • Weninger, Dieter & Wolsey, Laurence A., 2023. "Benders-type branch-and-cut algorithms for capacitated facility location with single-sourcing," European Journal of Operational Research, Elsevier, vol. 310(1), pages 84-99.
    • Handle: RePEc:eee:ejores:v:310:y:2023:i:1:p:84-99
    DOI: 10.1016/j.ejor.2023.02.042
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    1. Holmberg, Kaj & Ronnqvist, Mikael & Yuan, Di, 1999. "An exact algorithm for the capacitated facility location problems with single sourcing," European Journal of Operational Research, Elsevier, vol. 113(3), pages 544-559, March.
    2. Pasquale Avella & Maurizio Boccia, 2009. "A cutting plane algorithm for the capacitated facility location problem," Computational Optimization and Applications, Springer, vol. 43(1), pages 39-65, May.
    3. 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.
    4. J A Díaz & E Fernández, 2002. "A Branch-and-Price algorithm for the Single Source Capacitated Plant Location Problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(7), pages 728-740, July.
    5. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    6. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2021. "Benders decomposition for a stochastic three-level lot sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 291(1), pages 206-217.
    7. Ceyhan, Gökhan & Köksalan, Murat & Lokman, Banu, 2022. "Extensions for Benders cuts and new valid inequalities for solving the European day-ahead electricity market clearing problem efficiently," European Journal of Operational Research, Elsevier, vol. 300(2), pages 713-726.
    8. 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.
    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. Simon Görtz & Andreas Klose, 2012. "A Simple but Usually Fast Branch-and-Bound Algorithm for the Capacitated Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 597-610, November.
    11. Sune Lauth Gadegaard & Andreas Klose & Lars Relund Nielsen, 2018. "An improved cut-and-solve algorithm for the single-source capacitated facility location problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 1-27, March.
    12. Yang, Zhen & Chu, Feng & Chen, Haoxun, 2012. "A cut-and-solve based algorithm for the single-source capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 221(3), pages 521-532.
    13. Guastaroba, G. & Speranza, M.G., 2014. "A heuristic for BILP problems: The Single Source Capacitated Facility Location Problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 438-450.
    14. René Brandenberg & Paul Stursberg, 2021. "Refined cut selection for benders decomposition: applied to network capacity expansion problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 383-412, December.
    15. WENINGER Dieter, & WOLSEY, Laurence,, 2019. "Benders’ algorithm with (mixed)-integer subproblems," LIDAM Discussion Papers CORE 2019020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. R. K. Ahuja & J. B. Orlin & S. Pallottino & M. P. Scaparra & M. G. Scutellà, 2004. "A Multi-Exchange Heuristic for the Single-Source Capacitated Facility Location Problem," Management Science, INFORMS, vol. 50(6), pages 749-760, June.
    17. 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.
    18. Iván Contreras & Juan Díaz, 2008. "Scatter search for the single source capacitated facility location problem," Annals of Operations Research, Springer, vol. 157(1), pages 73-89, January.
    19. Fischetti, Matteo & Ljubić, Ivana & Sinnl, Markus, 2016. "Benders decomposition without separability: A computational study for capacitated facility location problems," European Journal of Operational Research, Elsevier, vol. 253(3), pages 557-569.
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