In this paper the authors consider the m-median and m-center problems on a network, subject to zone-type constraints. These constraints require that at least one server be located in each one of several prespecified zones that may overlap. The zones may be municipal districts, geographical zones, equity-type zones and so on. Special cases of the proble include the m-medi-center problem and the m-center (or m-median) problem with user-dependent distance constraints. The paper includes a relaxation algorithm where in each step of the algorithm a relaxed problem is solved. For the m-center problem wtih user-dependent distance constraints the relaxation algorithm can be refined by taking advantage of an available method to solve the relaxed problem. Computational experience suggests that the algorithm performs well for large problems.
