An Approach to Location Models Involving Sets as Existing Facilities

In this paper, we deal with single facility location problems in a general normed space in which the existing facilities are represented by convex sets of points. The criterion to be satisfied by the service facility is the minimization of an increasing, convex function of the distances from the service facility to the closest point of each demand set. We obtain a geometrical characterization of the set of optimal solutions for this problem. Two remarkable cases—the classical Weber problem and the minimax problem with demand sets—are studied as particular instances of our problem. Finally, for the planar polyhedral case, we give an algorithm to find the solution set of the considered problems.