Distance measure and the $$p$$p-median problem in rural areas

The $$p$$p-median model is used to locate $$P$$P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronizes the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling et al. (Ann Oper Res 201(1):83–97, 2012) compared two network distances with the Euclidean in a rural region with a sparse, heterogeneous network and a non-symmetric distribution of the population. For a coarse network and $$P$$P small, they found, in contrast to the literature, the Euclidean distance to be problematic. In this paper we extend their work by use of a refined network and study systematically the case when $$P$$P is of varying size (1–100 facilities). We find that the network distance give almost as good a solution as the travel-time network. The Euclidean distance gives solutions some 2–13 % worse than the network distances, and the solutions tend to deteriorate with increasing $$P$$P. Our conclusions extend to intra-urban location problems.