Proportionally Fairer Public Service Systems Design

Abstract

This paper focuses on the utilitarian solution of public service system design problem, obtained when maximising the sum of all utilities and proportionally fair-like solution, taking into account proportional changes in individual utilities. As an archetypal example of the optimisation problem, we are examining the weighted p-median problem, which is solved by the primary-dual based procedure. We use realistic largescale data describing the road network and spatial distribution of population. By comparing the resulting solutions, for selected range of parameters, we evaluate how costly it is to consider fairness criteria in the service system design. As for integer problems the proportional fairness scheme does not guarantee the existence of dominant optimal solution, we evaluate the close neighbourhood of obtained solutions. Based on these analyses we draw conclusions on the price of (proportionally-like) fair solutions and their stability.