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Minimax and maximin facility location problems on a sphere

Author

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  • Zvi Drezner
  • George O. Wesolowsky

Abstract

The problem dealt with in this article is as follows. There are n “demand points” on a sphere. Each demand point has a weight which is a positive constant. A facility must be located so that the maximum of the weighted distances (distances are the shortest arcs on the surface of the sphere) is minimized; this is called the minimax problem. Alternatively, in the maximin problem, the minimum weighted distance is maximized. A setup cost associated with each demand point may be added for generality. It is shown that any maximin problem can be reparametrized into a minimax problem. A method for finding local minimax points is described and conditions under which these are global are derived. Finally, an efficient algorithm for finding the global minimax point is constructed.

Suggested Citation

  • Zvi Drezner & George O. Wesolowsky, 1983. "Minimax and maximin facility location problems on a sphere," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 305-312, June.
    • Handle: RePEc:wly:navlog:v:30:y:1983:i:2:p:305-312
    DOI: 10.1002/nav.3800300211
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    Citations

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    Cited by:

    1. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2023. "Obnoxious facility location in multiple dimensional space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-354, July.
    2. Minnie H. Patel & Deborah L. Nettles & Stuart J. Deutsch, 1993. "A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 543-552, June.
    3. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
    4. Mordechai Jaeger & Jeff Goldberg, 1997. "Polynomial algorithms for center location on spheres," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(4), pages 341-352, June.
    5. Franco Rubio-López & Obidio Rubio & Rolando Urtecho Vidaurre, 2023. "The Inverse Weber Problem on the Plane and the Sphere," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    6. Zvi Drezner, 1988. "Location strategies for satellites' orbits," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 503-512, October.
    7. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.
    8. Drezner, Zvi & Kalczynski, Pawel & Salhi, Said, 2019. "The planar multiple obnoxious facilities location problem: A Voronoi based heuristic," Omega, Elsevier, vol. 87(C), pages 105-116.
    9. Pawel Kalczynski & Zvi Drezner, 2021. "The obnoxious facilities planar p-median problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 577-593, June.

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