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On the Set of Optimal Points to the Weber Problem

Author

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  • Zvi Drezner

    (Department of Management Science, California State University, Fullerton, Fullerton, California)

  • A. J. Goldman

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

It is known that the planar Weber location problem with l p distances has all its solutions in the convex hull of the demand points. for l 1 and l ∞ distances, additional conditions are known which reduce the set of possible optimal points to the intersection of that convex hull, the efficient set, and the points defined by a certain grid. In this paper, we determine the smallest set which includes at least one optimal point for every Weber problem based on a given set of demand points. It is shown that for 1 p p =1 or p =∞ the known conditions do not necessarily yield the correct set. Finally, we find the smallest possible set for p =1 or p =∞.

Suggested Citation

  • Zvi Drezner & A. J. Goldman, 1991. "On the Set of Optimal Points to the Weber Problem," Transportation Science, INFORMS, vol. 25(1), pages 3-8, February.
    • Handle: RePEc:inm:ortrsc:v:25:y:1991:i:1:p:3-8
    DOI: 10.1287/trsc.25.1.3
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