Balancing Service Efficiency and Equality in Location Models:Research Progress and Prospects
Efficiency and equity are two most important concepts in public services.Public facility locations play a critical role in the delivery of quality services in a convenient and equitable manner.In this paper,the facility location problems considering efficiency and equity are reviewed,and the further research on equitable aggregation functions is suggested.Firstly,the concepts of service equity,spatial equity,and service efficiency in public services are analyzed.The commonly used indicators of spatial equity are redefined mathematically by introducing the weight of service demand.Secondly,according to the key principles of model formulation,three approaches to handle spatial equity of service in location modeling are briefly summarized.The first approach directly uses one of the inequality indicators,as an objective or a constraint,in the mathematical model.Based on Rawls'fairness principle of"veil of ignorance",the second approach uses a well-designed ordered weighted distance function to construct an order median model.Following the sociological principle of"inequity aversion",the third approach uses equitable aggregation functions that take into account both efficiency and equity concerns.The monotonicity,anonymity,and Pigou-Dalton principles of transfers are the essential standards to formulate an equitable aggregation function.An aggregation function that weakly satisfies monotonicity,or the Pigou-Dalton principle of transfers is also acceptable in facility location modeling.Thirdly,several research directions are suggested to overcome the limitations of existing location models.Based on the concept of spatial envy of service,a general inequity-averse aggregation function,which weakly satisfies the criteria of equitable aggregation,is recommended for public facility location modeling.Theoretical analysis shows that the aggregation function has serval advantages:easy to formulate a new location model,relatively easy to solve the new model,and effective to increase the spatial equity by slightly increasing the average travel distance.Finally,it is encouraged to explore the general relationships between service cost,spatial access to service,and spatial equity,which are fundamental for public service evaluation,improvement,and decision making.
public servicelocation problemspatial equalitymathematical modelequitable aggregation func-tionsspatial envyPigou-Dalton principle of transfersimproved P-median problem
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