On the distribution approach to location problems

While making location decisions, the distribution of travel distances among the service recipients (clients) is an important issue. It is usually tackled with the minimax (center) or the minisum (median) solution concepts. Both concepts minimize only simple scalar characteristics of the distribution: the maximal distance and the average distance, respectively. In this paper, all the distances for the individual clients are considered as a set of multiple uniform criteria to be minimized. This results in a multiple criteria model taking into account the entire distribution of distances. Our analysis of the multiple criteria problem focuses on the symmetrically efficient solutions which comply with minimization of distances as well as with impartial consideration of the clients. Various solution concepts generating symmetrically efficient location patterns are analyzed. Finally, the reference distribution approach is developed as an interactive technique which enables us to identify a satisfactory symmetrically efficient location pattern by evolving a reference (target) distribution of distances.