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A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold

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  • Wuyang Yu

Abstract

When consumers are faced with the choice of competitive chain facilities that offer exclusive services, current rules do not properly describe the behavior pattern of these consumers. To eliminate the gap between the current rules and this kind of customers behavior pattern, the partially proportional rule with a threshold is proposed in this paper. A leader-follower model for discrete competitive facility location problem is established under the partially proportional rule with a threshold. Combining with the greedy strategy and the 2-opt strategy, a heuristical algorithm (GFA) is designed to solve the follower’s problem. By embedding the algorithm (GFA), an improved ranking-based algorithm (IRGA) is proposed to solve the leader-follower model. Numerical tests show that the algorithm proposed in this paper can solve the leader-follower model for discrete competitive facility location problem effectively. The effects of different parameters on the market share captured by the leader firm and the follower firm are analyzed in detail using a quasi-real example. An interesting finding is that in some cases the leader firm does not have a first-mover advantage.

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  • Wuyang Yu, 2019. "A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.
    • Handle: RePEc:plo:pone00:0225693
    DOI: 10.1371/journal.pone.0225693
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    1. Daniel Serra & Rosa Colomé, 2001. "articles: Consumer choice and optimal locations models: Formulations and heuristics," Papers in Regional Science, Springer;Regional Science Association International, vol. 80(4), pages 439-464.
    2. Zhang, Ying & Snyder, Lawrence V. & Ralphs, Ted K. & Xue, Zhaojie, 2016. "The competitive facility location problem under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 453-473.
    3. 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.
    4. Fernández, José & Hendrix, Eligius M.T., 2013. "Recent insights in Huff-like competitive facility location and design," European Journal of Operational Research, Elsevier, vol. 227(3), pages 581-584.
    5. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    6. Casas-Ramírez, Martha-Selene & Camacho-Vallejo, José-Fernando & Martínez-Salazar, Iris-Abril, 2018. "Approximating solutions to a bilevel capacitated facility location problem with customer's patronization toward a list of preferences," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 369-386.
    7. Timothy J. Gilbride & Greg M. Allenby, 2004. "A Choice Model with Conjunctive, Disjunctive, and Compensatory Screening Rules," Marketing Science, INFORMS, vol. 23(3), pages 391-406, October.
    8. R. Suárez-Vega & D. Santos-Peñate & P. Dorta-González, 2004. "Discretization and resolution of the (r|X p )-medianoid problem involving quality criteria," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 111-133, June.
    9. Kung, Ling-Chieh & Liao, Wei-Hung, 2018. "An approximation algorithm for a competitive facility location problem with network effects," European Journal of Operational Research, Elsevier, vol. 267(1), pages 176-186.
    10. Peter Peeters & Frank Plastria, 1998. "Discretization results for the Huff and Pareto-Huff competitive location models on networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 247-260, December.
    11. Rafael Suárez‐Vega & Dolores R. Santos‐Peñate & Pablo Dorta‐González, 2007. "The follower location problem with attraction thresholds," Papers in Regional Science, Wiley Blackwell, vol. 86(1), pages 123-137, March.
    12. ReVelle, C.S. & Eiselt, H.A. & Daskin, M.S., 2008. "A bibliography for some fundamental problem categories in discrete location science," European Journal of Operational Research, Elsevier, vol. 184(3), pages 817-848, February.
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