On the Set of Optimal Points to the Weber Problem

Zvi Drezner and A. J. Goldman
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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

Transportation Science, 1991, vol. 25, issue 1, 3-8

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 =∞.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:25:y:1991:i:1:p:3-8

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