Does Euclidian distance work when Location Models are applied in rural areas?

Abstract: Location Models are used to locate n service centers in order to serve a geographically distributed population. A cornerstone of such models is the measure of distance between the service center and a set of demand points, viz, the location of the population (customers, pupils, patients and so on). Evidence support the current practice of using the Euclidian distance. In this paper, we argue and provide empirical evidence that such a measure is misleading once the Location Models are applied to rural areas with heterogeneous transport networks and a uneven distributed population. This paper stems from the problem of finding an optimal allocation of a pre-specified number of hospitals in a large Swedish region with a low population density. We conclude that the Euclidian and the network distances based on a homogenous network (equal travel costs in the whole network) give approximately the same optimums. However network distances calculated from a heterogeneous network (different travel costs in different parts of the network) give widely different optimums when the number of hospitals increases. It is also shown that aggregating the population misplaces the hospitals by on average 25% (10 km)