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An Efficient Computational Procedure for the Rectilinear MAXIMIN Location Problem

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  • Emanuel Melachrinoudis

    (Northeastern University, Boston, Massachusetts 02115)

Abstract

This paper deals with the problem of locating a facility among n existing facilities so that the shortest weighted distance with respect to all existing facilities is as large as possible. The new facility is to be placed within a bounded convex region S in R 2 where the existing facilities also lie. The rectilinear distance is used for a distance metric. Applications of the model include the location of an undesirable or obnoxious facility in a bounded region in which the underlying distance metric is rectilinear. Based upon the linearization of the solution space an efficient algorithm is developed that finds the MAXIMIN point by solving a sequence of LPs using Simplex. Computational results are provided. The algorithm is shown to be computationally more efficient than an existing combinatorial algorithm. The use of the algorithm is illustrated in a numerical example.

Suggested Citation

  • Emanuel Melachrinoudis, 1988. "An Efficient Computational Procedure for the Rectilinear MAXIMIN Location Problem," Transportation Science, INFORMS, vol. 22(3), pages 217-223, August.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:3:p:217-223
    DOI: 10.1287/trsc.22.3.217
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    Cited by:

    1. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    2. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. D Nadirler & E Karasakal, 2008. "Mixed integer programming-based solution procedure for single-facility location with maximin of rectilinear distance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 563-570, April.
    4. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.

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