MINIMIZING QUANTILES SHARE RATIO IN MULTIPLE FACILITY LOCATION PROBLEM WITH TOTAL DISTANCE CONSTRAINT

Abstract

In this paper, we propose a multiple facility location problem to minimize inequality in distances to facilities. The inequality is evaluated by Quantiles Share Ratio (QsSR) that is a generalized version of Quintile Share Ratio (QSR). QSR is an inequality measure of income distribution defined as the ratio of total income received by the 20% of the population with the highest income (top quintile) to that received by the 20% of the population with the lowest income (lowest quintile). Drezner et al. (2014) have proposed single facility location problems using QSR where the inequality in distances to the facility is considered and the value of QSR is analytically derived at specific points such as the center of a circle and a rectangle, and vertices of a rectangle. Also, the paper mainly focuses on single facility location problems. In this paper, we develop a mathematical programming model seeking locations that minimize QsSR and propose a binary search method to solve the model. Furthermore, we extend the model by incorporating a total distance constraint. The models are applied to the case study of Arakawa ward in Tokyo using geographical and population data. Results show that our model provides low inequality locations with small increase in the total distance compared with the locations that minimize the total distance.