Computational study of radial approach to public service system design with generalized utility

This contribution deals with the problem of designing the optimal structure of most public service systems, where the total discomfort of all users is to be minimized. Such combinatorial problems are often formulated as weighted p-median problem described by a location-allocation model. Real instances are characterized by considerably big number of possible service center locations, which may take the value of several thousands. In such cases, the exact algorithm embedded into universal optimization tools for the location-allocation model usually fails due to enormous computational time or huge memory demands. Mentioned weakness can be overcome by approximate covering approach based on a radial formulation of the problem. This method constitutes such solving technique, which can be easily implemented within commercial IP-solver and enables to solve huge instances in admissible time. The generalized system utility studied in this paper follows the idea that the individual users utility comes from more than one located service center. This approach constitutes an extension of previously developed methods, where only one nearest center was taken as a source of individual users utility. Hereby, we study and compare both exact and radial approaches from the point of their impact on the solution accuracy and saved computational time.