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Aggregation Error Bounds for a Class of Location Models

Author

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  • R. L. Francis

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • T. J. Lowe

    (College of Business Administration, University of Iowa, Iowa City, Iowa 52242)

  • Arie Tamir

    (Department of Statistics & Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel)

Abstract

Many location models involve distances and demand points in their objective function. In urban contexts, there can be millions of demand points. This leads to demand point aggregation, which produces error. We identify a general model structure that includes most such location models, and present a means of obtaining error bounds for all models with this structure. The error bounds suggest how to do the demand point aggregation so as to keep the error small.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:294-307
    DOI: 10.1287/opre.48.2.294.12382
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    Cited by:

    1. Dominique Peeters & Isabelle Thomas, 2005. "Does the Shape of a Territory Influence the Locations of Human Activities? a Numerical Geography Approach," ERSA conference papers ersa05p56, European Regional Science Association.
    2. H. Emir-Farinas & R. Francis, 2005. "Demand Point Aggregation for Planar Covering Location Models," Annals of Operations Research, Springer, vol. 136(1), pages 175-192, April.
    3. R.L. Francis & T.J. Lowe & M.B. Rayco & A. Tamir, 2003. "Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 614-637, September.
    4. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    5. Irawan, Chandra Ade & Salhi, Said & Scaparra, Maria Paola, 2014. "An adaptive multiphase approach for large unconditional and conditional p-median problems," European Journal of Operational Research, Elsevier, vol. 237(2), pages 590-605.
    6. Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
    7. Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    8. Kalcsics, Jörg & Nickel, Stefan & Puerto, Justo & Rodríguez-Chía, Antonio M., 2010. "Distribution systems design with role dependent objectives," European Journal of Operational Research, Elsevier, vol. 202(2), pages 491-501, April.
    9. Robert Aboolian & Oded Berman & Dmitry Krass, 2012. "Profit Maximizing Distributed Service System Design with Congestion and Elastic Demand," Transportation Science, INFORMS, vol. 46(2), pages 247-261, May.
    10. M T Lucas & D Chhajed, 2004. "Applications of location analysis in agriculture: a survey," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 561-578, June.
    11. 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.
    12. 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.
    13. Brotcorne, Luce & Laporte, Gilbert & Semet, Frederic, 2003. "Ambulance location and relocation models," European Journal of Operational Research, Elsevier, vol. 147(3), pages 451-463, June.
    14. Afshartous, David & Guan, Yongtao & Mehrotra, Anuj, 2009. "US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1086-1096, August.
    15. Francis, R. L. & Lowe, T. J. & Tamir, A. & Emir-Farinas, H., 2004. "A framework for demand point and solution space aggregation analysis for location models," European Journal of Operational Research, Elsevier, vol. 159(3), pages 574-585, December.
    16. Nickel, Stefan & Velten, Sebastian, 2017. "Optimization problems with flexible objectives: A general modeling approach and applications," European Journal of Operational Research, Elsevier, vol. 258(1), pages 79-88.

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