In this paper we study the following general MaxMinoptimization problem concerning undesirable (obnoxious) facility location: Given a set of n sites S inside a convex region P, construct m garbage deposit sites V _m such that the minimum distance between these sites V _m and the union of S and V _m , V _m ∪S, is maximized. We present a general method using Voronoi diagrams to approximately solve two such problems when the sites S’s are points and weighted convex polygons (correspondingly, V _m’s are points and weighted points and the distances are L ₂ and weighted respectively). In the latter case we generalize the Voronoi diagrams for disjoint weighted convex polygons in the plane. Our algorithms run in polynomial time and approximate the optimal solutions of the above two problems by a factor of 2.