PLANAR POINT-OBJECTIVE LOCATION-PROBLEMS WITH NONCONVEX CONSTRAINTS - A GEOMETRICAL CONSTRUCTION

The planar point-objective location problem has attracted considerable interest among Location Theory researchers. The result has been a number of papers giving properties or algorithms for particular instances of the problem. However, most of these results are only valid when the feasible region where the facility is to be located is the whole space R2, which is a rather inaccurate approximation in many real world location problems. In this paper, the feasible region is allowed to be any closed, not necessarily convex, set S in R2. The special structure of this nonconvex vector-optimization problem is exploited, leading to a geometrical resolution procedure when the feasible region S can be decomposed into a finite number of (not necessarily disjoint) polyhedra.