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Worst-case analysis of demand point aggregation for the Euclidean p-median problem

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  • Qi, Lian
  • Shen, Zuo-Jun Max

Abstract

Solving large-scale p-median problems is usually time consuming. People often aggregate the demand points in a large-scale p-median problem to reduce its problem size and make it easier to solve. Most traditional research on demand point aggregation is either experimental or assuming uniformly distributed demand points in analytical studies. In this paper, we study demand point aggregation for planar p-median problem when demand points are arbitrarily distributed. Efficient demand aggregation approaches are proposed with the corresponding attainable worst-case aggregation error bounds measured. We demonstrate that these demand aggregation approaches introduce smaller worst-case aggregation error bounds than that of the honeycomb heuristic [Papadimitriou, C.H., 1981. Worst-case and probabilistic analysis of a geometric location problem. SIAM Journal on Computing 10, 542-557] when demand points are arbitrarily distributed. We also conduct numerical experiments to show their effectiveness.

Suggested Citation

  • Qi, Lian & Shen, Zuo-Jun Max, 2010. "Worst-case analysis of demand point aggregation for the Euclidean p-median problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 434-443, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:434-443
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    References listed on IDEAS

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    1. Zhao, Peiwu & Batta, Rajan, 1999. "Analysis of centroid aggregation for the Euclidean distance p-median problem," European Journal of Operational Research, Elsevier, vol. 113(1), pages 147-168, February.
    2. Frank Plastria, 2001. "On the choice of aggregation points for continuousp-median problems: A case for the gravity centre," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 217-242, December.
    3. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    4. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.
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    4. John Gunnar Carlsson & Fan Jia, 2013. "Euclidean Hub-and-Spoke Networks," Operations Research, INFORMS, vol. 61(6), pages 1360-1382, December.

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    Aggregation Error bounds p-Median;

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