Analysis of centroid aggregation for the Euclidean distance p-median problem

Demand data aggregation results in loss of information and thereby induces errors in the locational decision being made, both in the facility location configurations (optimality error) and in the computed value of the objective function (cost error). The aggregation effect is quite problem-specific, depending on the aggregation scheme used and on the demand pattern. In this paper, we perform a theoretical analysis for the centroid aggregation effect on the Euclidean distance p-median location problem. We study the worst case and average case errors, and in the multi-facility location model Source C error is closely examined. The results of the paper are illustrated via numerical examples and some empirical findings of previous work are interpreted using our analytical results.