Reducing disparities in transportation distance in a stochastic facility location problem

Abstract

This paper focuses on improving equity in a well-known stochastic facility location problem (FLP). Specifically, given sets of potential facility locations and customers with random demand, traditional stochastic optimization models for the FLP seek to determine the number and location of facilities to open that minimize the total cost, including the fixed cost of opening facilities, expected transportation cost from customers to facilities, and expected unmet demand cost. We show that such models lead to inequitable distribution of facilities across different regions and disparities in transportation distance needed to reach those facilities. To mitigate such disparities, we first analyze a set of measures to gauge the level of equity of location decisions. Then, to investigate the impact of the method of modeling uncertainty on equity, we formulate and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models that employ these measures to minimize disparities in transportation distance needed to access open facilities, assuming known and unknown distributions of the demand. Finally, we use a case study based on the Lehigh region in Pennsylvania to compare the impact of location decisions obtained using the traditional and the proposed models on equity and efficiency. Our results demonstrate how different methods of modeling equity under uncertainty can result in different location decisions with varying impacts on equity and efficiency. Notably, while prior literature shows that equity-neutral DRO models for the FLP yield robust location decisions, our results additionally demonstrate that the proposed DRO models produce equitable distributions of facilities and more effectively mitigate disparities in transportation distance than their SP and equity-neutral counterparts.