Analysis of aggregation errors for the p-median problem

Data aggregation in location problems is a common issue which, on one hand, reduces the problem size, but, on the other hand, results in loss of information and solution errors. In this paper, we study aggregation errors in the case of the p-median problem where the objective is to select p facilities from n demand points, and to allocate demand points to facilities, to minimize the total travel distance. The aggregation literature in location analysis has identified three different sources of error. In this paper, we introduce a number of other error sources, many resulting from poor choices made by analysts at different stages of the analysis. Using enumeration data from Edmonton, we investigate how aggregation causes individual solutions of a p-median problem to move up or down in the rankings of all feasible solutions. We also pose the aggregation/location process as a 2-step optimization problem, describe the role of the aggregation method and level in this process, and experimentally show how the method and level affect the resulting aggregation errors. Based on our analysis, we propose some guidelines for aggregating spatial population data for the p-median problem.