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A parallelized Lagrangean relaxation approach for the discrete ordered median problem

Author

Listed:
  • Juana L. Redondo

    (Universidad de Almería)

  • Alfredo Marín

    (Universidad de Murcia)

  • Pilar M. Ortigosa

    (Universidad de Almería)

Abstract

We study a flexible discrete location model which has as particular cases the $$p$$ p -median problem, the $$p$$ p -center problem and the $$k$$ k -centrum problem, among many others, called the discrete ordered median problem. A previous formulation is adapted and a Lagrangean relaxation is carried out on this formulation in order to produce lower and upper bounds on the optimal value of the problem. The relaxed problem can be split into several subproblems whose resolution is simultaneously tackled by means of a parallelized algorithm. The results are compared to other methods proposed in the literature for this problem.

Suggested Citation

  • Juana L. Redondo & Alfredo Marín & Pilar M. Ortigosa, 2016. "A parallelized Lagrangean relaxation approach for the discrete ordered median problem," Annals of Operations Research, Springer, vol. 246(1), pages 253-272, November.
    • Handle: RePEc:spr:annopr:v:246:y:2016:i:1:d:10.1007_s10479-014-1744-x
    DOI: 10.1007/s10479-014-1744-x
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    References listed on IDEAS

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    1. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    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. Puerto, Justo & Pérez-Brito, Dionisio & García-González, Carlos G., 2014. "A modified variable neighborhood search for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 234(1), pages 61-76.
    4. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    5. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    6. Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    7. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
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    Cited by:

    1. Enrique Domínguez & Alfredo Marín, 2020. "Discrete ordered median problem with induced order," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 793-813, October.
    2. Schryen, Guido, 2020. "Parallel computational optimization in operations research: A new integrative framework, literature review and research directions," European Journal of Operational Research, Elsevier, vol. 287(1), pages 1-18.

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