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Gradual cover competitive facility location

Author

Listed:
  • Tammy Drezner

    (California State University-Fullerton)

  • Zvi Drezner

    (California State University-Fullerton)

  • Pawel Kalczynski

    (California State University-Fullerton)

Abstract

A new gradual cover competitive facility location model is proposed and tested. In cover competitive models, it is assumed that up to a certain distance a demand point is attracted to a facility and beyond this distance it is not. The decline in attraction and cover is abrupt. It is either 0 or 1. We propose a gradual decline in attraction from 1 to 0. As the distance increases the attraction and cover decline. The buying power captured by a facility cannot exceed its attraction level, and the total buying power captured by all facilities cannot exceed the buying power available at the demand point. The single-facility location is optimally solved. The largest problem of 1000 demand points is solved in less than one second. The multiple facility version is solved by SNOPT and other solvers.

Suggested Citation

  • Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2020. "Gradual cover competitive facility location," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 333-354, June.
    • Handle: RePEc:spr:orspec:v:42:y:2020:i:2:d:10.1007_s00291-020-00585-x
    DOI: 10.1007/s00291-020-00585-x
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    References listed on IDEAS

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    1. David L. Huff, 1966. "A Programmed Solution for Approximating an Optimum Retail Location," Land Economics, University of Wisconsin Press, vol. 42(3), pages 293-303.
    2. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    3. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    4. T Drezner & Z Drezner & P Kalczynski, 2012. "Strategic competitive location: improving existing and establishing new facilities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(12), pages 1720-1730, December.
    5. Eiselt, H.A. & Marianov, Vladimir, 2009. "Gradual location set covering with service quality," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 121-130, June.
    6. T Drezner & Z Drezner & P Kalczynski, 2011. "A cover-based competitive location model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 100-113, January.
    7. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    8. Drezner, Zvi, 1982. "Competitive location strategies for two facilities," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 485-493, November.
    9. H. A. Eiselt & Vladimir Marianov & Tammy Drezner, 2015. "Competitive Location Models," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 365-398, Springer.
    10. Frank A. Fetter, 1924. "The Economic Law of Market Areas," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 38(3), pages 520-529.
    11. Tammy Drezner & Zvi Drezner & Zvi Goldstein, 2010. "A stochastic gradual cover location problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 367-372, June.
    12. T Drezner & Z Drezner, 2012. "Modelling lost demand in competitive facility location," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(2), pages 201-206, February.
    13. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    14. H. A. Eiselt, 2011. "Equilibria in Competitive Location Models," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 139-162, Springer.
    15. D Serra & H A Eiselt & G Laporte & C S ReVelle, 1999. "Market Capture Models under Various Customer-Choice Rules," Environment and Planning B, , vol. 26(5), pages 741-750, October.
    16. Drezner, Zvi & Kalczynski, Pawel & Salhi, Said, 2019. "The planar multiple obnoxious facilities location problem: A Voronoi based heuristic," Omega, Elsevier, vol. 87(C), pages 105-116.
    17. Oded Berman & Zvi Drezner & Dmitry Krass, 2019. "The multiple gradual cover location problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(6), pages 931-940, June.
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    Cited by:

    1. Tammy Drezner & Morton O’Kelly & Zvi Drezner, 2023. "Multipurpose shopping trips and location," Annals of Operations Research, Springer, vol. 321(1), pages 191-208, February.
    2. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    3. Zvi Drezner & Dawit Zerom, 2024. "A refinement of the gravity model for competitive facility location," Computational Management Science, Springer, vol. 21(1), pages 1-18, June.

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