Testing the gravity pp-median model empirically

Regarding the location of a facility, the presumption in the widely used pp-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity pp-median model offers an extension to the pp-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the pp-median model. We found, however, the gravity pp-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the pp-median model, or it gives unstable solutions due to a non-concave objective function.