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This article deals with the location problem for balancing the serviceefficiency and equality. In public service systems, some people may feel envyin case that they need longer travel distance to access services than others.The strength of the envy can be measured by comparing one's travel distance toservice facility with a threshold distance. Using the total envy function, fourextended p-median problems are proposed for trade-off between serviceefficiency and equality. Five analytical properties of the new problems aremathematically proven. The new problems were tested on three sets ofwell-designed instances. The experimentation shows that the equality measures,such as the standard deviation, the mean absolute deviation, and the Ginicoefficient between travel distances, can be substantially improved byminimizing the travel cost and the spatial envy. The experimentation also showsthat, when the service supply is given in terms of the number of facilities,the service equality can be considerably improved by slightly increasing thetravel distance. When the service supply is increased in terms of the number offacilities, both the service efficiency and spatial equality can besignificantly improved.

Extended p-median problems for balancing service efficiency and equality