The single facility location problem with average-distances

This paper considers a location problem in ℝ ⁿ , where the demand is not necessarily concentrated at points but it is distributed in hypercubes following a Uniform probability distribution. The goal is to locate a service facility minimizing the weighted sum of average distances (measured with ℓ _p norms) to these demand hypercubes. In order to do that, we present an iterative scheme that provides a sequence converging to an optimal solution of the problem for p∈1,2]. For the planar case, analytical expressions of this iterative procedure are obtained for p=2 and p=1, where two different approaches are proposed. The paper ends with a computational analysis of the proposed methodology, comparing its efficiency with a standard minimizer.