A Modified Gravity p-Median Model for Optimizing Facility Locations

The gravity -median model is an important improvement to the widely-used -median model. However, there is still a debate on its validity in empirical applications. Previous studies even doubt the significance of the gravity -median model. Using a case study of tertiary hospitals in Shenzhen, China, this study re-examines the difference between the gravity -median model with the -median model, by decomposing the difference between the two models into gravity rule and variant attraction. This study also proposes a modified gravity -median model by incorporating a distance threshold. The empirical results support the validity of the gravity -median model, and also reveal that only when the attractions of candidate facility locations are variable will the gravity -median model lead to different results with the -median model. The difference between the modified gravity -median model and the gravity -median model is also examined. Moreover, the impacts of the distance-decay parameter and distance threshold on solutions are investigated. Results indicate that a larger distance-decay parameter tends to result in a more dispersed distribution of optimal facilities and a smaller average travel time, and a smaller distance threshold can better promote the spatial equity of facilities. The proposed method can also be applied in studies of other types of facilities or in other areas.