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A cut-and-solve based algorithm for the single-source capacitated facility location problem

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  • Yang, Zhen
  • Chu, Feng
  • Chen, Haoxun

Abstract

In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS’s branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0–1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented.

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  • 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.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:3:p:521-532
    DOI: 10.1016/j.ejor.2012.03.047
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    2. 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.
    3. Corberán, Ángel & Landete, Mercedes & Peiró, Juanjo & Saldanha-da-Gama, Francisco, 2020. "The facility location problem with capacity transfers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    4. Di Francesco, Massimo & Gaudioso, Manlio & Gorgone, Enrico & Murthy, Ishwar, 2021. "A new extended formulation with valid inequalities for the Capacitated Concentrator Location Problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 975-986.
    5. Yang, Zhen & Chen, Haoxun & Chu, Feng & Wang, Nengmin, 2019. "An effective hybrid approach to the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 467-480.
    6. Guazzelli, Cauê Sauter & Cunha, Claudio B., 2018. "Exploring K-best solutions to enrich network design decision-making," Omega, Elsevier, vol. 78(C), pages 139-164.
    7. 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.
    8. Chandra Ade Irawan & Martino Luis & Said Salhi & Arif Imran, 2019. "The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem," Annals of Operations Research, Springer, vol. 275(2), pages 367-392, April.
    9. 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.
    10. Raghavan, S. & Sahin, Mustafa & Salman, F. Sibel, 2019. "The capacitated mobile facility location problem," European Journal of Operational Research, Elsevier, vol. 277(2), pages 507-520.
    11. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2021. "On single-source capacitated facility location with cost and fairness objectives," European Journal of Operational Research, Elsevier, vol. 289(3), pages 959-974.

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