Minimax and maximin facility location problems on a sphere

Zvi Drezner and George O. Wesolowsky

Naval Research Logistics Quarterly, 1983, vol. 30, issue 2, 305-312

Abstract: The problem dealt with in this article is as follows. There are n “demand points” on a sphere. Each demand point has a weight which is a positive constant. A facility must be located so that the maximum of the weighted distances (distances are the shortest arcs on the surface of the sphere) is minimized; this is called the minimax problem. Alternatively, in the maximin problem, the minimum weighted distance is maximized. A setup cost associated with each demand point may be added for generality. It is shown that any maximin problem can be reparametrized into a minimax problem. A method for finding local minimax points is described and conditions under which these are global are derived. Finally, an efficient algorithm for finding the global minimax point is constructed.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:30:y:1983:i:2:p:305-312

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