The inverse minisum circle location problem

Let n weighted points be given in the plane. The inverse version of the minisum circle location problem deals with modifying the weights of points with minimum cost, such that the sum of the weighted distances from the circumference of a given circle C with radius r, to the given points is minimized. The classical model of this problem contains infinite constraints. In this paper, a mathematical model with finite constraints is presented. Then an efficient method is developed for solving this problem.