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Aggregation Error Bounds for a Class of Location Models

Author

Listed:
  • 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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    References listed on IDEAS

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    1. R. L. Francis & T. J. Lowe & M. B. Rayco, 1996. "Row-Column Aggregation for Rectilinear Distance p -Median Problems," Transportation Science, INFORMS, vol. 30(2), pages 160-174, May.
    2. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    3. Ananth V. Iyer & H. Donald Ratliff, 1990. "Accumulation Point Location on Tree Networks for Guaranteed Time Distribution," Management Science, INFORMS, vol. 36(8), pages 958-969, August.
    4. Paul D. Domich & Karla L. Hoffman & Richard H. F. Jackson & Marjorie A. McClain, 1991. "Locating Tax Facilities: A Graphics-Based Microcomputer Optimization Model," Management Science, INFORMS, vol. 37(8), pages 960-979, August.
    5. Justin C. Williams, 1995. "Political Redistricting: A Review," Papers in Regional Science, Wiley Blackwell, vol. 74(1), pages 13-40, January.
    6. Erkut, Erhan & Neuman, Susan, 1989. "Analytical models for locating undesirable facilities," European Journal of Operational Research, Elsevier, vol. 40(3), pages 275-291, June.
    7. J. N. Hooker & R. S. Garfinkel & C. K. Chen, 1991. "Finite Dominating Sets for Network Location Problems," Operations Research, INFORMS, vol. 39(1), pages 100-118, February.
    8. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    9. Andreatta, G. & Mason, F., 1985. "k-eccentricity and absolute k-centrum of a probabilistic tree," European Journal of Operational Research, Elsevier, vol. 19(1), pages 114-117, January.
    10. Ashok Kumar & Leroy B. Schwarz & James E. Ward, 1995. "Risk-Pooling Along a Fixed Delivery Route Using a Dynamic Inventory-Allocation Policy," Management Science, INFORMS, vol. 41(2), pages 344-362, February.
    11. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    12. Hau L. Lee & Corey Billington & Brent Carter, 1993. "Hewlett-Packard Gains Control of Inventory and Service through Design for Localization," Interfaces, INFORMS, vol. 23(4), pages 1-11, August.
    13. Gabriel Y. Handler, 1985. "Medi-Centers of a Tree," Transportation Science, INFORMS, vol. 19(3), pages 246-260, August.
    14. Oded Berman & David Simchi-Levi, 1990. "Technical Note—Conditional Location Problems on Networks," Transportation Science, INFORMS, vol. 24(1), pages 77-78, February.
    15. Jonathan Halpern, 1978. "Finding Minimal Center-Median Convex Combination (Cent-Dian) of a Graph," Management Science, INFORMS, vol. 24(5), pages 535-544, January.
    16. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    17. Mirchandani, Pitu B. & Odoni, Amedeo R., 1979. "Locating new passenger facilities on a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 13(2), pages 113-122, June.
    18. D. R. Shier & P. M. Dearing, 1983. "Optimal Locations for a Class of Nonlinear, Single-Facility Location Problems on a Network," Operations Research, INFORMS, vol. 31(2), pages 292-303, April.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    14. 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.
    15. 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.
    16. 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.

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