Abstract
In large scale location-allocation studies it is necessary to use data-aggregation in order to obtain solvable models. A detailed analysis is given of the errors induced by this aggregation in the evaluation of thep-median objective function. Then it is studied how to choose the points at which to aggregate given groups of demand points so as to minimise this aggregation error. Forp-median problems with euclidean distances, arguments are given in favour of the centre of gravity of the groups. These arguments turn out to be much stronger for rectangular distance. Aggregating at the centroid also leads to much higher precision bounds on the errors for rectangular distance. Some numerical results are obtained validating the theoretical developments.
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This research was partially done while the author was on visit at the Laboratoire d’Analyse Appliquée et Optimisation at the Université de Bourgogne, Dijon, France. Thanks to E. Carrizosa, B. Rayco and four anonymous referees for many thoughtful remarks.
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Plastria, F. On the choice of aggregation points for continuousp-median problems: A case for the gravity centre. Top 9, 217–242 (2001). https://doi.org/10.1007/BF02579084
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DOI: https://doi.org/10.1007/BF02579084