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Minimax Multifacility Location with Euclidean Distances

Author

Listed:
  • Jack Elzinga

    (The Johns Hopkins University, Baltimore, Maryland)

  • Donald Hearn

    (University of Florida, Gainesville, Florida)

  • W. D. Randolph

    (Washington, D. C.)

Abstract

The problem considered is that of locating N new facilities among M existing facilities with the objective of minimizing the maximum weighed Euclidean distance among all facilities. The application of nonlinear duality theory shows this problem can always be solved by maximizing a continuously differentiable concave objective subject to a small number of linear constraints. This leads to a solution procedure which produces very good numerical results. Computational experience is reported.

Suggested Citation

  • Jack Elzinga & Donald Hearn & W. D. Randolph, 1976. "Minimax Multifacility Location with Euclidean Distances," Transportation Science, INFORMS, vol. 10(4), pages 321-336, November.
    • Handle: RePEc:inm:ortrsc:v:10:y:1976:i:4:p:321-336
    DOI: 10.1287/trsc.10.4.321
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    Cited by:

    1. Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.
    2. Brazil, M. & Ras, C.J. & Thomas, D.A., 2014. "A geometric characterisation of the quadratic min-power centre," European Journal of Operational Research, Elsevier, vol. 233(1), pages 34-42.
    3. Cavalier, Tom M. & Conner, Whitney A. & del Castillo, Enrique & Brown, Stuart I., 2007. "A heuristic algorithm for minimax sensor location in the plane," European Journal of Operational Research, Elsevier, vol. 183(1), pages 42-55, November.
    4. R. Chen & G. Y. Handler, 1987. "Relaxation method for the solution of the minimax location‐allocation problem in euclidean space," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 775-788, December.

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