Abstract
This paper considers a location problem in ℝn, 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.
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Valero Franco, C., Rodríguez-Chía, A.M. & Espejo Miranda, I. The single facility location problem with average-distances. TOP 16, 164–194 (2008). https://doi.org/10.1007/s11750-008-0040-9
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DOI: https://doi.org/10.1007/s11750-008-0040-9