In the standard location problem, the authors are required to locate m new facilities and to allocate the demands from n fixed points (or customers) among them in order to minimize a sum of transportation costs. An important assumption is that each new facility has a known, fixed capacity to service demands. Often the capacity is assumed to be infinite so that the demands are simply allocated to the nearest facility. In this paper, an extension of the basic model is developed in which the number of new facilities and their capacities are treated as decision variables. A set-up cost is added in the objective function for each facility. This set-up is assumed to be a concave function of capacity, in order to account for economies of scale which are realized from building larger facilities. Thus, the new model allows us to determine the optimal trade-off between set-up costs and transportation costs. Some properties of the model are investigated, and solution procedures are suggested.
