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Letter to the Editor—Some Aspects of a Minimax Location Problem

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  • Richard L. Francis

    (The Ohio Stale University, Columbus, Ohio)

Abstract

Some aspects of a minimax version of the Steiner-Weber location problem are studied. A necessary condition is given for a minimax location, or solution; a lower bound on the value of a minimax solution is given that is attained for many problems; and an explicit minimax solution is given for the case where the lower bound is attained. Also, a geometric characterization of the minimax solution is discussed, and a closely related facility design problem is examined.

Suggested Citation

  • Richard L. Francis, 1967. "Letter to the Editor—Some Aspects of a Minimax Location Problem," Operations Research, INFORMS, vol. 15(6), pages 1163-1169, December.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:6:p:1163-1169
    DOI: 10.1287/opre.15.6.1163
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    Cited by:

    1. 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.
    2. Piyush Kumar & E. Alper Yıldırım, 2009. "An Algorithm and a Core Set Result for the Weighted Euclidean One-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 614-629, November.
    3. Mark E. Cawood & P. M. Dearing, 2024. "The weighted Euclidean one-center problem in $${\mathbb {R}}^n$$ R n," Computational Optimization and Applications, Springer, vol. 89(2), pages 553-574, November.
    4. Jack Brimberg & Robert F. Love, 1991. "Estimating travel distances by the weighted lp norm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 241-259, April.
    5. M. T. Ko & R. C. T. Lee & J. S. Chang, 1990. "Rectilinear m‐Center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 419-427, June.
    6. Wei-jie Cong & Le Wang & Hui Sun, 2020. "Rank-two update algorithm versus Frank–Wolfe algorithm with away steps for the weighted Euclidean one-center problem," Computational Optimization and Applications, Springer, vol. 75(1), pages 237-262, January.
    7. L. Frießs & K. Klamroth & M. Sprau, 2005. "A Wavefront Approach to Center Location Problems with Barriers," Annals of Operations Research, Springer, vol. 136(1), pages 35-48, April.

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