Letter to the Editor—A Localization Theorem for Optimal Facility Placement

Abstract

The problem is that of locating a facility in a region, so as to minimize the weighted sum of distances between customers and facility. This note shows that a subregion containing half or more of the total “customer-weight,” if it obeys an additional restrictive hypothesis, must include at least one optimal location for the facility. Thus the search for an optimal location can be limited to such a subregion, once identified.