The obnoxious facilities planar p-median problem

In this paper, we propose the planar obnoxious facilities 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 communities 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 communities because they generate nuisance affecting these communities. The resulting problem is extremely non-convex and traditional nonlinear 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, showing the trade-off between the required distance and the p-median objective, to assist the planers in making location decisions.