A minimum-envy location problem for spatial equality of public service: model formulation and case analysis

Subjects: Geosciences >> Geography Subjects: Mathematics >> Control and Optimization. submitted time 2023-05-13

Yunfeng Kong Shiyan Zhai

Abstract： Location problems have been widely applied to service planning of public health, compulsory education, emergency management, and delivery logistics. However, the mainstream location models are usually to optimize the efficiency objectives such as travel cost, facility cost and the number of customs to be served, rather than the equality objectives. A few location models aim to optimize one of the equality measures, such as the variance of distances, the deviation of distances, the Gini coefficient between the travel distances, and the variance of spatial accessibility indexes. However, the facility locations, capacities and their service areas can be easily distorted by most equality-oriented objective functions. In this paper, a spatially envy objective function for service equality is proposed to overcome the shortcomings of commonly used equality functions. The envy value of customers at a location is determined by their travel distance that beyond a predefined distance. The envy function can be added to mainstream location models in a weighted manner. As a result, the capacitated p-median problem (CPMP) is enhanced as CPMP-envy. The original and improved models were tested on three large instances. Case experiments show that the equality measures, such as maximum travel distance, variance of distances, coefficient of variation, and Gini coefficient between travel distances, can be substantially improved by minimizing the weighted sum of spatial envy and travel cost. It is argued that the envy indicator has theoretical and practical potentials in facility planning towards spatial equality of public service.

Peer Review Status:Awaiting Review

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