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Competitive facility location under attrition

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  • Zvi Drezner

    (California State University-Fullerton)

  • Dawit Zerom

    (California State University-Fullerton)

Abstract

In this paper we address the possibility that in a competitive facility location model, one of the existing competing facilities will go out of business. We find the best location for a new facility protecting against such a possibility. Four commonly used decision rules (optimistic, pessimistic, minimax regret, and expected value) are analyzed and optimally solved within a given relative accuracy. The results of extensive computational experiments are reported. Special upper bounds, that may be a basis for other optimization problems, are designed. They are much tighter than existing lower bounds. The number if iterations is reduced by a factor close to 5000, and consequently run times were improved by about the same factor. The largest instance of 10 existing competing facilities and 20,000 demand points was solved in less than one second by each of the four decision criteria. The idea of possible scenarios can be investigated by other models in future research.

Suggested Citation

  • Zvi Drezner & Dawit Zerom, 2023. "Competitive facility location under attrition," Computational Management Science, Springer, vol. 20(1), pages 1-19, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00473-z
    DOI: 10.1007/s10287-023-00473-z
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    References listed on IDEAS

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    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. Tammy Drezner & Zvi Drezner, 2004. "Finding the optimal solution to the Huff based competitive location model," Computational Management Science, Springer, vol. 1(2), pages 193-208, July.
    3. Tammy Drezner, 2009. "Location of retail facilities under conditions of uncertainty," Annals of Operations Research, Springer, vol. 167(1), pages 107-120, March.
    4. Tammy Drezner & Zvi Drezner & Dawit Zerom, 2020. "Facility Dependent Distance Decay in Competitive Location," Networks and Spatial Economics, Springer, vol. 20(4), pages 915-934, December.
    5. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location and design problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 40-62, October.
    6. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    7. Tammy Drezner & Zvi Drezner & Dawit Zerom, 2022. "An extension of the gravity model," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(12), pages 2732-2740, December.
    8. Richard L. Church, 2019. "Understanding the Weber Location Paradigm," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Contributions to Location Analysis, chapter 0, pages 69-88, Springer.
    9. John Hodgson, M., 1981. "The location of public facilities intermediate to the journey to work," European Journal of Operational Research, Elsevier, vol. 6(2), pages 199-204, February.
    10. 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.
    11. 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.
    12. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location model with concave demand," European Journal of Operational Research, Elsevier, vol. 181(2), pages 598-619, September.
    13. Robert Aboolian & Oded Berman & Dmitry Krass, 2009. "Efficient solution approaches for a discrete multi-facility competitive interaction model," Annals of Operations Research, Springer, vol. 167(1), pages 297-306, March.
    14. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2022. "Multiple obnoxious facilities with weighted demand points," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(3), pages 598-607, March.
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    Cited by:

    1. Pawel Kalczynski & Zvi Drezner & Morton O’Kelly, 2025. "Multi-facility location models incorporating multipurpose shopping trips," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(2), pages 455-475, June.

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