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.

Elements of simulated annealing in Pareto front search

“…The fair objective function value f2(y) formulated by ( 3) expresses the number of users, whose time distance from the nearest located service facility exceeds given limit D. This objective follows the request of certain level of fairness in access to the provided service [5,18,22,23].…”

“…Analogically, let APF denote the area of the complete Pareto front. Then the value of gap can be computed in percentage by (5).…”

Re-Aggregation Heuristics for the Large Location Problems with Lexicographic Minimax Objective

“…Alternatively, there is also another fairness criterion known as a proportional fairness. Solutions provided with respect to this criterion tend to achieve higher system efficiency, for more details see reference [14].…”

Min-Max Optimization of Emergency Service System by Exposing Constraints

“…Fairness in general emerges whenever limited resources are to be fairly distributed among participants [9], [10], [11] and [12]. The strongest scheme is so-called lexicographic min-max criterion.…”