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A Cut Approach to the Rectilinear Distance Facility Location Problem

Author

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  • Jean-Claude Picard

    (Ecole Polytechnique, Montreal, Quebec)

  • H. Donald Ratliff

    (University of Florida, Gainesville, Florida)

Abstract

This paper is concerned with the problem of locating n new facilities in the plane when there are m facilities already located. The objective is to minimize the weighted sum of rectilinear distances. Necessary and sufficient conditions for optimality are established. We show that the optimum locations of the new facilities are dependent on the relative orderings of old facilities along the two coordinate axes but not on the distances between them. Based on these results an algorithm is presented that requires the solution of at most m − 1 minimum cut problems on networks with at most n + 2 vertices. All of these results are easily extended to the same location problem on a tree graph.

Suggested Citation

  • Jean-Claude Picard & H. Donald Ratliff, 1978. "A Cut Approach to the Rectilinear Distance Facility Location Problem," Operations Research, INFORMS, vol. 26(3), pages 422-433, June.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:3:p:422-433
    DOI: 10.1287/opre.26.3.422
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    Cited by:

    1. Dilip Chhajed & Timothy J. Lowe, 1998. "Solving a selected class of location problems by exploiting problem structure: A decomposition approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 791-815, December.
    2. Sarker, Bhaba R. & Wilhelm, Wilbert E. & Hogg, Gary L., 1998. "One-dimensional machine location problems in a multi-product flowline with equidistant locations," European Journal of Operational Research, Elsevier, vol. 105(3), pages 401-426, March.

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