<p>This article deals with the location problem for balancing service efficiency and equality. In public service systems, some individuals may experience envy if they must travel longer distances to access services compared to others. This envy can be redefined by comparing an individual’s travel distance to a service facility with a threshold distance. Based on the newly defined envy function, four extended p-median problems are proposed to balance service efficiency and spatial equality. The new objective function is designed to be inequity-averse and exhibits several analytical properties related 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 experiments demonstrate that the equality measures, such as the standard deviation, mean absolute deviation, and Gini coefficient between travel distances, can be significantly improved with only a slight increase in travel distance. Additionally, the advantages of the extended problems were validated through Pareto optimality analysis and comparisons with other location problems.</p>