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Heuristic Procedures for Solving the Discrete Ordered Median Problem

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  • Patricia Domínguez-Marín
  • Stefan Nickel
  • Pierre Hansen
  • Nenad Mladenović

Abstract

We present two heuristic methods for solving the Discrete Ordered Median Problem (DOMP), for which no such approaches have been developed so far. The DOMP generalizes classical discrete facility location problems, such as the p-median and p-center. The first procedure proposed in this paper is based on a genetic algorithm developed by Moreno Vega (1996) for p-median and p-center problems. Additionally, a second heuristic approach based on the Variable Neighborhood Search metaheuristic (VNS) proposed by Hansen and Mladenović (1997) for the p-median problem is described. An extensive numerical study is presented to show the efficiency of both heuristics and compare them. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:145-173:10.1007/s10479-005-2043-3
    DOI: 10.1007/s10479-005-2043-3
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    References listed on IDEAS

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    1. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    2. Antonio M. Rodríguez-Chía & Stefan Nickel & Justo Puerto & Francisco R. Fernández, 2000. "A flexible approach to location problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(1), pages 69-89, February.
    3. Sourour Elloumi & Martine Labbé & Yves Pochet, 2004. "A New Formulation and Resolution Method for the p-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 84-94, February.
    4. Beasley, J. E., 1985. "A note on solving large p-median problems," European Journal of Operational Research, Elsevier, vol. 21(2), pages 270-273, August.
    5. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.
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    Cited by:

    1. Paola Festa & Panos Pardalos, 2012. "Efficient solutions for the far from most string problem," Annals of Operations Research, Springer, vol. 196(1), pages 663-682, July.
    2. Olender, Paweł & Ogryczak, Włodzimierz, 2019. "A revised Variable Neighborhood Search for the Discrete Ordered Median Problem," European Journal of Operational Research, Elsevier, vol. 274(2), pages 445-465.
    3. Ting L. Lei & Richard L. Church, 2014. "Vector Assignment Ordered Median Problem," International Regional Science Review, , vol. 37(2), pages 194-224, April.
    4. Stanimirovic, Zorica & Kratica, Jozef & Dugosija, Djordje, 2007. "Genetic algorithms for solving the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 182(3), pages 983-1001, November.
    5. Jörg Kalcsics & Stefan Nickel & Justo Puerto & Antonio Rodríguez-Chía, 2010. "The ordered capacitated facility location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 203-222, July.
    6. Kalcsics, Jörg & Nickel, Stefan & Puerto, Justo & Rodríguez-Chía, Antonio M., 2010. "Distribution systems design with role dependent objectives," European Journal of Operational Research, Elsevier, vol. 202(2), pages 491-501, April.
    7. Rodríguez-Chía, Antonio M. & Espejo, Inmaculada & Drezner, Zvi, 2010. "On solving the planar k-centrum problem with Euclidean distances," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1169-1186, December.
    8. Víctor Blanco, 2019. "Ordered p-median problems with neighbourhoods," Computational Optimization and Applications, Springer, vol. 73(2), pages 603-645, June.
    9. Martínez-Merino, Luisa I. & Albareda-Sambola, Maria & Rodríguez-Chía, Antonio M., 2017. "The probabilistic p-center problem: Planning service for potential customers," European Journal of Operational Research, Elsevier, vol. 262(2), pages 509-520.
    10. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    11. Samuel Deleplanque & Martine Labbé & Diego Ponce & Justo Puerto, 2020. "A Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 582-599, July.

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