New error bounds in continuous minisum location for aggregation at the gravity centre (Q2708109)

When dealing with large-scale location problems it is often necessary to use the data in an aggregated form. In this paper results for the continuous single-facility location problem are derived where the subdivision of the demand points into aggregation groups is given. The aggregation error is defined as the difference between the objective value of the optimal solution for the unaggregated and the aggregated data. First the case with only one aggregation group is discussed. Here asymptotic results for the case where distances are measured by general gauges are derived motivating the use of the centre of gravity as the aggregation point. Also, special theorems for the block norm case are presented. The asymptotic analysis gives some information about the effect on the aggregation error if points far away from the aggregation centre are chosen. Results for the non-asymptotic situation are also stated. Bounds on the aggregation error are given for the case of aggregation at any point and for the case of aggregation at the centre of gravity. Again, depending on the structure of the gauges, several results are presented. The paper is clearly written and extends known results in this area.