Aggregation and surrogation error in the \(p\)-median model (Q1417704)

The \(p\)-median model locates \(p\) facilities within a given finite set minimising the weighted sum of distances of demand points to the closest facility. Aggregation errors arise when demand points are aggregated, e.g. for privacy reasons or to reduce the problem size. Surrogation errors are due to replacement of the true demand by easier available surrogate values. This paper reports on experimental results obtained for both types of errors on a large geographical dataset. These suggest that surrogate data available at low aggregation level may be advantageously used to de-aggregate the actual demand data available only at higher aggregation levels, and allows to lower the aggregation errors considerably. This seems to hold both for exact as for heuristic solution methods.