Row-Column Aggregation for Rectilinear Distance p-Median Problems

Richard L. Francis · Timothy J. Lowe · M. Brenda Rayco

40 citations0/0 files storedTransportation Science

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Abstract

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.

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References

1963Location-Allocation Problems 1978Errors in measuring distances from populations to service centers 1985Using Block Norms for Location Modeling 1979The Aggregation Problem in Location‐Allocation 1991Improved complexity bounds for location problems on the real line 1987Elimination of Source A and B Errors in p‐Median Location Problems 1992Strategies for Solving Large Location-Allocation Problems by Heuristic Methods 1989Aggregation effects in maximum covering models

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2009Aggregation in hub location problems 2014An adaptive multiphase approach for large unconditional and conditional p-median problems 1999Analysis of centroid aggregation for the Euclidean distance p-median problem 2011Evaluating representation and scale error in the maximal covering location problem using GIS and intelligent areal interpolation 1998Aggregation method experimentation for large-scale network location problems 2013

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