Multi-facility location using a maximin criterion and rectangular distances

A branch and bound algorithm is suggested to solve the maximin multiple facilities rectilinear distance location problem with distance constraints. This problem is a continuous version of the p anti-center dispersion problem. The branch and bound algorithm borrows ideas from the Drezner-Wesolowsky algorithm and the improvements suggested by Mehrez, Sinuany-Stern and Stulman to solve the single facility maximin rectilinear problem. An important observation is that the multiple facility problem can be solved in polynomial time with respect to the number of demand points.