Extended p-median problems for balancing service efficiency and equality

This article deals with the location problem for balancing the service efficiency and equality. In public service systems, some individuals may experience envy if they have to travel longer distances to access services compared to others. This envy can be simplified by comparing an individual's travel distance to a service facility against a threshold distance. Four extended p-median problems are proposed, utilizing the total travel distance and total envy to balance service efficiency and spatial equality. The new objective function is designed to be inequity-averse and exhibits several analytical properties that pertain to both service efficiency and equality. The extended problems were extensively tested on two sets of benchmark instances and one set of geographical instances. The experimentation shows that the equality measures, such as the standard deviation, mean absolute deviation, and Gini coefficient between travel distances, can be substantially improved by slightly increasing the travel distance. Additionally, the advantages of the proposed problems were validated through Pareto optimality analysis and comparisons with other location problems.