Equivalence of Solutions to Network Location Problems

Abstract

This paper compares solution concepts associated with three location problems on a network: (i) a single-facility distance minimization problem; (ii) a two-facility spatial competition problem; and (iii) a single-facility locational voting problem. It is shown that the three problems have a common global solution when the network exhibits a property of symmetry around a point. For more general networks, this ceases to be true for global solutions but an identity holds for local solutions.