Comparing the p-median and flow-refueling models for locating alternative-fuel stations

The p-median and flow-refueling models are two of the more popular models for optimal location of alternative-fuel stations. The p-median model, one of the most widely used location models of any kind, locates p facilities and allocates demand nodes to them to minimize total weighted distance traveled. In comparison, the flow-refueling location model (FRLM) is a path-based demand model that locates p stations to maximize the number of trips on their shortest paths that can be refueled. For a path to be considered refuelable, one or more stations must be located on the path in a way that allows the round trip to be completed without running out of fuel, given the vehicle driving range. In this paper, we analyze how well the facilities located by each model perform on the other's objective function on road networks in Florida. While each objective function degrades somewhat when facilities are located by the other model, the stations located by the flow-refueling model generally do better on the p-median objective than the stations located by the p-median model do on the flow-refueling objective. This difference between the two models is even more pronounced at the state scale than at the metropolitan scale. In addition, the optimal locations for the FRLM tend to be more much more stable as p increases than those located by the p-median model.