  In this paper we propose the planar obnoxious p-median problem. In the
p-median problem the objective is to find p locations for facilities that
minimize the weighted sum of distances between demand points and their closest
facility. In the obnoxious version we add constraints that each facility must
be located at least a certain distance from a partial set of demand points
because they generate nuisance affecting these demand points. The resulting
problem is extremely non-convex and traditional non-linear solvers such as
SNOPT are not efficient. An efficient solution method based on Voronoi diagrams
is proposed and tested. We also constructed the efficient frontiers of the test
problems to assist the planers in making location decisions.
