Planar maximal covering with ellipses

We consider a maximal covering location problem on the plane, where the objective is to provide maximal coverage of weighted demand points using a set of ellipses at minimum cost. The problem involves selecting k out of in ellipses. The problem occurs naturally in wireless telecommunications networks as coverage from some transmission towers takes an elliptical shape. A mixed integer nonlinear programming formulation (MINLP) for the problem is presented but MINLP solvers fail to solve it in a reasonable time. We suggest a Simulated Annealing heuristic as an alternate approach for solving the problem. Our computational results employing the heuristic show very good results with efficient processing times. We also discuss an extension to the problem where coverage occurs on a spherical surface and show that it can be solved with the same heuristic. (c) 2008 Elsevier Ltd. All rights reserved.