Solving infinite p-center problems in Euclidean space using an interactive graphical method

An algorithm is developed for the location of p service centers with one or more continuous demand areas. The method is based on the repeated solution of finite relaxation problems. Due to the infinite number of demand points distributed on arbitrarily shaped, bounded regions, an interactive computer graphical method is utilized. Here, the user has to determine the initial points to be included in the relaxation set, to inspect on the screen at each stage whether a displayed solution as demonstrated by circles covering the given demand region, is feasible, and if not, to choose a "good' demand point to be added to the relaxation set. Using a desktop PC, various problems were solved including locating optimally up to four centers over the area of Israel as a demand region. -Authors