Efficient Points in Location Problems

Abstract

Much of the literature involving the location of one or more new facilities in the plane is concerned with minimizing a single objective function. In this paper we consider the problem of generating the efficient set of locations for a single facility where it is important that the facility be located as close as possible to each of a number of existing facilities whose locations are known. We concentrate on the notion of distance commonly referred to as the ℓ₁ norm, the Manhattan norm, or the city-block norm but results for other norms are given also. We develop properties of the efficient set and present two separate procedures for generating the efficient set.