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A cover-based competitive location model

Author

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  • T Drezner

    (Steven G. Mihaylo College of Business and Economics, California State University–Fullerton)

  • Z Drezner

    (Steven G. Mihaylo College of Business and Economics, California State University–Fullerton)

  • P Kalczynski

    (Steven G. Mihaylo College of Business and Economics, California State University–Fullerton)

Abstract

In this paper we propose a new approach to estimating market share captured by competing facilities. The approach is based on cover location models. Each competing facility has a ‘sphere of influence’ determined by its attractiveness level. More attractive facilities have a larger radius of the sphere of influence. The buying power of a customer within the sphere of influence of several facilities is equally divided among the competing facilities. The buying power of a customer within the sphere of influence of no facility is lost. Assuming the presence of competition in the area, the objective is to add a number of new facilities to a chain of existing facilities in such a way that the increase of market share captured by the chain is maximized. The model is formulated and analysed. Optimal and heuristic solution algorithms are designed. Computational experiments demonstrate the effectiveness of the proposed algorithms.

Suggested Citation

  • 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.
  • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:1:d:10.1057_jors.2009.153
    DOI: 10.1057/jors.2009.153
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    References listed on IDEAS

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    1. 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.
    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. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    5. T Drezner & Z Drezner, 2008. "Lost demand in a competitive environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 362-371, March.
    6. 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.
    7. Nesterov, Y. & Nemirovskii, A., 1995. "An interior-point method for generalized linear-fractional programming," LIDAM Reprints CORE 1168, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Drezner, Tammy & Drezner, Zvi & Salhi, Said, 2002. "Solving the multiple competitive facilities location problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 138-151, October.
    9. Michael B. Teitz & Polly Bart, 1968. "Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph," Operations Research, INFORMS, vol. 16(5), pages 955-961, October.
    10. Drezner, Zvi, 1982. "Competitive location strategies for two facilities," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 485-493, November.
    11. Watson-Gandy, C. D. T., 1982. "Heuristic procedures for the m-partial cover problem on a plane," European Journal of Operational Research, Elsevier, vol. 11(2), pages 149-157, October.
    12. Leonardi, Giorgio & Tadei, Roberto, 1984. "Random utility demand models and service location," Regional Science and Urban Economics, Elsevier, vol. 14(3), pages 399-431, August.
    13. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    14. Drezner, Zvi, 1986. "The p-cover problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 312-313, August.
    15. Zvi Drezner & George O. Wesolowsky & Tammy Drezner, 2004. "The gradual covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 841-855, September.
    16. Osman Alp & Erhan Erkut & Zvi Drezner, 2003. "An Efficient Genetic Algorithm for the p-Median Problem," Annals of Operations Research, Springer, vol. 122(1), pages 21-42, September.
    17. Danny Z. Chen & Ovidiu Daescu & Yang Dai & Naoki Katoh & Xiaodong Wu & Jinhui Xu, 2005. "Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions, with Applications," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 69-90, February.
    18. Berman, Oded & Drezner, Zvi, 2008. "The p-median problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 189(1), pages 19-30, August.
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    Cited by:

    1. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    2. Tammy Drezner & Zvi Drezner & Dawit Zerom, 2023. "The Obnoxious Competitive Facility Location Model," Networks and Spatial Economics, Springer, vol. 23(4), pages 885-903, December.
    3. Christian Burkart & Pamela C. Nolz & Walter J. Gutjahr, 2017. "Modelling beneficiaries’ choice in disaster relief logistics," Annals of Operations Research, Springer, vol. 256(1), pages 41-61, September.
    4. 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.
    5. 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.
    6. Mejía, Gonzalo & Aránguiz, Raúl & Espejo-Díaz, Julián Alberto & Granados-Rivera, Daniela & Mejía-Argueta, Christopher, 2023. "Can street markets be a sustainable strategy to mitigate food insecurity in emerging countries? Insights from a competitive facility location model," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    7. 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.
    8. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2019. "A directional approach to gradual cover," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-93, April.

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