The Minisum and Minimax Location Problems Revisited

The minisum (minimax) problem consists of locating a single facility in the plane with the aim of minimizing the sum of the weighted distances (the maximum weighted distance) to m given points. We present two solution methods for generalized versions of these problems in which (i) location is restricted to the union of a finite number of convex polygons; (ii) distances are approximated by norms that may differ with the given points; and (iii) transportation costs are increasing and continuous functions of distance. Computational experience is described.