Price of Fairness in Public Service System Design

In the host situations, a public service system is designed so that the total disutility, like social costs, is minimized. The social costs are often proportional to the total distance travelled by all users to the nearest service center. This approach often causes such situation that the total social cost is minimal, but disutility of the worst situated user is extremely high, what is denoted as unfair system design. 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 disutility of better located users is optimized subject to the disutility of the worst situated users does not worsen, what is called lexicographical minimization. In this contribution we present an approximate approach based on radial formulation of the problem with homogenous system of radii given by dividing points. This approach will be used for both system optimal public service system design and the fair one with specific ways of dividing point deployment. In the computational study, we present the solution of several real instances and evaluate the price of fairness connected with two different designs.