On the structure of the solution set for the single facility location problem with average distances

Abstract

This paper analyzes continuous single facility location problems where the demand is randomly defined by a given probability distribution. For these types of problems that deal with the minimization of average distances, we obtain geometrical characterizations of the entire set of optimal solutions. For the important case of total polyhedrality on the plane we derive efficient algorithms with polynomially bounded complexity. We also develop a discretization scheme that provides $${\varepsilon}$$ -approximate solutions of the original problem by solving simpler location problems with points as demand facilities.