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On relaxing the integrality of the allocation variables of the reliability fixed-charge location problem

Author

Listed:
  • José L. Sainz-Pardo

    (Universidad Miguel Hernández)

  • Javier Alcaraz

    (Universidad Miguel Hernández)

  • Mercedes Landete

    (Universidad Miguel Hernández)

  • Juan F. Monge

    (Universidad Miguel Hernández)

Abstract

The aim of the reliability fixed-charge location problem is to find robust solutions to the fixed-charge location problem when some facilities might fail with probability q. In this paper we analyze for which allocation variables in the reliability fixed-charge location problem formulation the integrality constraint can be relaxed so that the optimal value matches the optimal value of the binary problem. We prove that we can relax the integrality of all the allocation variables associated to non-failable facilities or of all the allocation variables associated to failable facilities but not of both simultaneously. We also demonstrate that we can relax the integrality of all the allocation variables whenever a family of valid inequalities is added to the set of constraints or whenever the parameters of the problem satisfy certain conditions. Finally, when solving the instances in a data set we discuss which relaxation or which modification of the problem works better in terms of resolution time and we illustrate that relaxing the integrality of the allocation variables inappropriately can alter the objective value considerably.

Suggested Citation

  • José L. Sainz-Pardo & Javier Alcaraz & Mercedes Landete & Juan F. Monge, 2017. "On relaxing the integrality of the allocation variables of the reliability fixed-charge location problem," Journal of Global Optimization, Springer, vol. 67(4), pages 787-804, April.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:4:d:10.1007_s10898-016-0439-z
    DOI: 10.1007/s10898-016-0439-z
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    References listed on IDEAS

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    1. Elena Fernández & Mercedes Landete, 2015. "Fixed-Charge Facility Location Problems," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 47-77, Springer.
    2. Alfredo Marín & Stefan Nickel & Sebastian Velten, 2010. "An extended covering model for flexible discrete and equity location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 125-163, February.
    3. Mari'n, Alfredo & Canovas, Lazaro & Landete, Mercedes, 2006. "New formulations for the uncapacitated multiple allocation hub location problem," European Journal of Operational Research, Elsevier, vol. 172(1), pages 274-292, July.
    4. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.
    5. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
    6. Karen Aardal & Martine Labbé & Janny Leung & Maurice Queyranne, 1996. "On the Two-Level Uncapacitated Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 289-301, August.
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    Cited by:

    1. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F. & Sainz-Pardo, José L., 2020. "Multi-objective evolutionary algorithms for a reliability location problem," European Journal of Operational Research, Elsevier, vol. 283(1), pages 83-93.

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