Convex Location Problems on Tree Networks

P. M. Dearing, R. L. Francis and T. J. Lowe
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P. M. Dearing: Cornell University, Ithaca, New York
R. L. Francis: University of Florida, Gainesville, Florida
T. J. Lowe: University of Florida, Gainesville, Florida

Operations Research, 1976, vol. 24, issue 4, 628-642

Abstract: This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.

Date: 1976
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