Aggregation without Loss of Optimality in Competitive Location Models

Abstract

In the context of competitive facility location problems demand points often have to be aggregated due to computational intractability. However, usually this spatial aggregation biases the value of the objective function and the optimality of the solution cannot be guaranteed for the original model. We present a preprocessing aggregation method to reduce the number of demand points which prevents this loss of information, and therefore avoids the possible loss of optimality. It is particularly effective in the frequent situation with a large number of demand points and a comparatively low number of potential facility sites, and coverage defined by spatial nearness. It is applicable to any spatial consumer behaviour model of covering type. This aggregation approach is applied in particular to a Competitive Maximal Covering Location Problem and to a recently developed von Stackelberg model. Some empirical results are presented, showing that the approach may be quite effective.