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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. 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).
    3. Olivier Briant & Denis Naddef, 2004. "The Optimal Diversity Management Problem," Operations Research, INFORMS, vol. 52(4), pages 515-526, August.
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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. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.

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