Minimax Multifacility Location with Euclidean Distances

The problem considered is that of locating N new facilities among M existing facilities with the objective of minimizing the maximum weighed Euclidean distance among all facilities. The application of nonlinear duality theory shows this problem can always be solved by maximizing a continuously differentiable concave objective subject to a small number of linear constraints. This leads to a solution procedure which produces very good numerical results. Computational experience is reported.