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Multicriteria Planar Ordered Median Problems

Author

Listed:
  • S. Nickel

    (Saarland University)

  • J. Puerto

    (Universidad de Sevilla)

  • A. M. Rodríguez-Chía

    (Universidad de Cádiz)

  • A. Weissler

    (SAP AG)

Abstract

In this paper, we deal with the determination of the entire set of Pareto solutions of location problems involving Q general criteria. These criteria include median, center, or centdian objective functions as particular instances. We characterize the set of Pareto solutions of all these multicriteria problems for any polyhedral gauge. An efficient algorithm is developed for the planar case and its complexity is established. Extensions to the nonconvex case are also considered. The proposed approach is more general than previously published approaches to multicriteria location problems.

Suggested Citation

  • S. Nickel & J. Puerto & A. M. Rodríguez-Chía & A. Weissler, 2005. "Multicriteria Planar Ordered Median Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 657-683, September.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:3:d:10.1007_s10957-005-5502-8
    DOI: 10.1007/s10957-005-5502-8
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    Cited by:

    1. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    2. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    3. 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.
    4. 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.
    5. André Berger & Alexander Grigoriev & Andrej Winokurow, 2017. "An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions," Computational Optimization and Applications, Springer, vol. 68(3), pages 661-669, December.

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