Row-Column Aggregation for Rectilinear Distance p-Median Problems

For large-scale p-median problems, it is common to aggregate the demand points. This size reduction via aggregation makes the problem easier to solve, but introduces error. Doing this aggregation well is provably difficult. We present a median-row-column aggregation algorithm, MRC, with provable properties including an error bound, an (attainable) upper bound on the maximum objective function error. MRC adjusts spacing of individual rows and columns to exploit problem structure. For e demand points, r rows, and c columns, the algorithm has computational order e(c + r + log e), and order e storage requirements. We report encouraging computational experience.