The minimum<i>p</i>-envy location problem: a new model for equitable distribution of emergency resources

Abstract

Equity is an important consideration in public services such as Emergency Medical Service (EMS) systems. In such systems not only equitability but also performance depends on the spatial distribution of facilities and resources. This paper proposes the minimum p-envy facility location model which aims to find optimal locations for facilities in order to balance customers’ perceptions of equity in receiving service. The model is developed and evaluated through the lens of EMS systems, where ambulances are located at facilities (stations) with the objective of minimizing the sum of “envy” among all demand zones (customer points) with respect to an ordered set of p operating stations weighted by the proportion of demand in each zone. The problem is formulated as an integer program, with priority weights assigned according the probability that an ambulance is available, which is estimated using the hypercube model. Because of the computational effort required to obtain solutions using commercially available software, a tabu search is developed to solve the problem. A case study using real-world data is presented. The performance of the proposed model is tested and compared to other location models such as the p-center and maximal-covering-location problems (MCLP).