On the choice of aggregation points for continuous \(p\)-median problems: A case for the gravity centre
The author treats a specific problem in solving continuous location problems. To handle efficiently large scale location-allocation problems it is necessary to aggregate the underlying sets of real data (e.g. customer locations) to obtain solvable models. At first a detailed analysis of the errors (pure aggregation errors, allocation errors) induced by data-aggregation is given, which is applied to the \(p\)-median objective function. In the following part it is shown how to choose the points at which to aggregate given groups of demand points so as to minimize the aggregation error. For \(p\)-median problems with Euclidean distances, arguments are given in favor of the gravity center of the groups, but these turn out to be much stronger for rectangular distances. Aggregating at the centroid also leads to much higher precision bounds on the errors for rectangular distances. Finally the author shows some numerical results, which are obtained validating the theoretical developments.
scientific article; zbMATH DE number 1740553