Distance predicting functions and applied location-allocation models

Distances between demand points and potential sites for implementing facilities are essential inputs to location-allocation models. Computing actual road distances for a given problem can be quite burdensome since it involves digitalizing a network, while approximating these distances by l_p -norms, using for instance a geographical information system, is much easier. We may then wonder how sensitive the solutions of a location-allocation model are to the choice of a particular metric. In this paper, simulations are performed on a lattice of 225 points using the k-median problem. Systematic changes in p and in the orientation of the orthogonal reference axes are used. Results suggest that the solutions of the k-median are rather insensitive to the specification of the l_p -norm.