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Continuous Center Problems

In: Foundations of Location Analysis

Author

Listed:
  • Zvi Drezner

    (California State University-Fullerton)

Abstract

The minimax facility location problem (also called the one center problem) seeks to locate a facility so that the maximum distance to a set of demand points is minimized. Using Euclidean distances in the plane, this problem is equivalent to finding the center of the smallest circle enclosing all points, hence the term “center” regarding this problem. When other metrics are used, the 1-center problem is equivalent to covering all points with a shape similar to the unit ball of the metric. For example, when rectilinear distances are used, the problem is to cover all points with the smallest possible diamond.

Suggested Citation

  • Zvi Drezner, 2011. "Continuous Center Problems," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 63-78, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-7572-0_4
    DOI: 10.1007/978-1-4419-7572-0_4
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    Citations

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    Cited by:

    1. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    2. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.

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