This article deals with the location problem for balancing the service efficiency and equality. In public service systems, some people may feel envy in 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 to service facility with a threshold distance. Using the total envy function, four extended p-median problems are proposed for trade-off between service efficiency and equality. Five analytical properties of the new problems are mathematically proven. The new problems were tested on three sets of well-designed instances. The experimentation shows that the equality measures, such as the standard deviation, the mean absolute deviation, and the Gini coefficient between travel distances, can be substantially improved by minimizing the travel cost and the spatial envy. The experimentation also shows that, when the service supply is given in terms of the number of facilities, the service equality can be considerably improved by slightly increasing the travel distance. When the service supply is increased in terms of the number of facilities, both the service efficiency and spatial equality can be significantly improved.

翻译：本文研究旨在平衡服务效率与公平性的区位问题。在公共服务系统中，部分人群可能因需要更长出行距离才能获取服务而产生相对剥夺感。这种相对剥夺感的强度可通过比较个体出行距离与阈值距离进行度量。基于总相对剥夺感函数，本文提出四种扩展p-中位问题以权衡服务效率与公平性。通过数学推导证明了新问题的五个解析性质，并在三组精心设计的测试集上进行了实证检验。实验结果表明：通过最小化出行成本与空间相对剥夺感，可显著改善出行距离的标准差、平均绝对偏差及基尼系数等公平性指标。同时发现，在给定设施数量作为服务供给约束时，适度增加出行距离能有效提升服务公平性；而当通过增加设施数量来扩大服务供给时，服务效率与空间公平性均可获得显著提升。