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A tighter formulation of the p-median problem

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  • Sourour Elloumi

    (CEDRIC-CNAM)

Abstract

Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. It can be viewed as a variation of the uncapacitated facility location problem. We propose a new formulation of this problem by a mixed integer linear problem. We show that this formulation, while it has the same value by LP-relaxation, can be much more efficient than two previous formulations. The computational experiment performed on two sets of benchmark instances has showed that the efficiency of the standard branch-and-cut algorithm has been significantly improved. Finally, we explore the structure of the new formulation in order to derive reduction rules and to accelerate the LP-relaxation resolution.

Suggested Citation

  • Sourour Elloumi, 2010. "A tighter formulation of the p-median problem," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 69-83, January.
    • Handle: RePEc:spr:jcomop:v:19:y:2010:i:1:d:10.1007_s10878-008-9162-0
    DOI: 10.1007/s10878-008-9162-0
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    References listed on IDEAS

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    1. Richard Church, 2003. "COBRA: A New Formulation of the Classic p-Median Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 103-120, September.
    2. Olivier Briant & Denis Naddef, 2004. "The Optimal Diversity Management Problem," Operations Research, INFORMS, vol. 52(4), pages 515-526, August.
    3. CORNUEJOLS, Gérard & NEMHAUSER, George L. & WOLSEY, Laurence A., 1980. "A canonical representation of simple plant location problems and its applications," LIDAM Reprints CORE 414, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Sergio García & Martine Labbé & Alfredo Marín, 2011. "Solving Large p -Median Problems with a Radius Formulation," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 546-556, November.
    3. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    4. Boris Goldengorin & Dmitry Krushinsky & Jannes Slomp, 2012. "Flexible PMP Approach for Large-Size Cell Formation," Operations Research, INFORMS, vol. 60(5), pages 1157-1166, October.
    5. Kuzbakov, Yerlan & Ljubić, Ivana, 2024. "New formulations for two location problems with interconnected facilities," European Journal of Operational Research, Elsevier, vol. 314(1), pages 51-65.
    6. Caleb C. Fast & Illya V. Hicks, 2017. "A Branch Decomposition Algorithm for the p -Median Problem," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 474-488, August.
    7. Benati, Stefano & García, Sergio, 2012. "A p-median problem with distance selection," DES - Working Papers. Statistics and Econometrics. WS ws121913, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. 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.
    9. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.

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