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Single facility location problems with unbounded unit balls

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  • Y. Hinojosa
  • J. Puerto

Abstract

In this paper we consider a new class of continuous location problems where the “distances” are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where there exist zero-distance regions. We prove a geometrical characterization of these measures of distance as the length of shortest paths between points using only a subset of directions of their unit balls. We also characterize the complete set of optimal solutions for this class of continuous single facility location problems and we give resolution methods to solve them. Our analysis allows to consider new models of location problems and generalizes previously known results. Copyright Springer-Verlag 2003

Suggested Citation

  • Y. Hinojosa & J. Puerto, 2003. "Single facility location problems with unbounded unit balls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 87-104, September.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:1:p:87-104
    DOI: 10.1007/s001860300277
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    Cited by:

    1. Frank Plastria, 2009. "Asymmetric distances, semidirected networks and majority in Fermat–Weber problems," Annals of Operations Research, Springer, vol. 167(1), pages 121-155, March.
    2. Wanka, Gert & Bot, Radu Ioan & Vargyas, Emese, 2007. "Duality for location problems with unbounded unit balls," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1252-1265, June.
    3. Gert Wanka & Oleg Wilfer, 2017. "Duality results for nonlinear single minimax location problems via multi-composed optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 401-439, October.

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    Keywords

    Continuous location; Convex analysis;

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