Analysis of aggregation errors for the p-median problem

Abstract

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. Scope and purpose When selecting locations for facilities, such as schools, warehouses and retail outlets, one has to take into account the demand for the service provided by the facility. In many instances, such facilities serve a large number of individuals, and it may not be realistic to model each individual as a separate demand point. To reduce the problem size to a manageable one, an analyst is usually forced to aggregate the demand (population) data by representing a collection of individuals as one demand point. While this is a practical solution, it perturbs the original problem and may introduce errors to subsequent analysis. This paper focuses on such errors in the case of a popular facility location model. We take a critical look at the literature in this area, and observe that a significant portion of the errors reported in the past result from poor OR practice by the analyst in different phases of the problem solution. In our (limited) computational experience, errors introduced by aggregating demand data are very small. Based on our analysis, we provide some “do’s” and “don’ts” for spatial data aggregation for the model under consideration.