Exact and heuristic radial approach to fair public service system design

This paper deals with fair public service system design formulated as the weighted p-median problem minimizing the total disutility, like social costs. The social costs are often proportional to the total distance travelled by all users to the nearest located service center. The above objective denoted as min-sum criterion may cause such situation that the total social costs are minimal, but the disutility of the worst situated user is extremely high, what is considered unfair. A fair approach to the public service system design consists in the process, when the disutility of the worst situated users is minimized first and then the disutility of better located users is optimized subject to the disutility of the worst situated users does not worsen. Mathematical models of such public service system design are often related to the lexicographic p-median problem, where the numbers of served users and possible service center locations take the value of several hundreds or thousands. The necessity of solving large instances has led to the approximate approach based on a radial formulation. Hereby, we are presenting the approximate approach with homogenous system of radii given by dividing points applied to fair public service system design. Special attention is paid to the first phase of the process, which consists in minimizing the disutility of the worst situated users.