Fixed Point Optimality Criteria for the Location Problem with Arbitrary Norms

Abstract

The single-facility location problem in continuous space is considered, with distances given by arbitrary norms. When distances are Euclidean, for many practical problems the optimal location of the new facility coincides with one of the existing facilities. This property carries over to problems with generalized distances. In this paper a necessary and sufficient condition for the location of an existing facility to be the optimal location of the new facility is developed. Some computational examples using the condition are given.