Convex Location Problems on Tree Networks

Dearing, P. M.; Francis, R. L.; Lowe, T. J.
July 1976
Operations Research;Jul/Aug76, Vol. 24 Issue 4, p628
Academic Journal
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 and convex sets are identified.


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