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Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution

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  • Küçükaydin, Hande
  • Aras, Necati
  • Kuban AltInel, I.

Abstract

We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at predetermined candidate sites. We employ Huff's gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find the optimal solution of this model, we convert it into an equivalent one-level mixed-integer nonlinear program so that it can be solved by global optimization methods. Apart from reporting computational results obtained on a set of randomly generated instances, we also compute the benefit the leader firm derives from anticipating the competitor's reaction of adjusting the attractiveness levels of its facilities. The results on the test instances indicate that the benefit is 58.33% on the average.

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  • Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:3:p:206-220
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    1. Lederer, Phillip J & Hurter, Arthur P, Jr, 1986. "Competition of Firms: Discriminatory Pricing and Location," Econometrica, Econometric Society, vol. 54(3), pages 623-640, May.
    2. 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.
    3. José Fernández & Blas Pelegrín & Frank Plastria & Boglárka Tóth, 2007. "Planar Location and Design of a New Facility with Inner and Outer Competition: An Interval Lexicographical-like Solution Procedure," Networks and Spatial Economics, Springer, vol. 7(1), pages 19-44, March.
    4. 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.
    5. Jan, Rong-Hong & Chern, Maw-Sheng, 1994. "Nonlinear integer bilevel programming," European Journal of Operational Research, Elsevier, vol. 72(3), pages 574-587, February.
    6. Aras, Necati & Aksen, Deniz & Gönül Tanugur, Ayse, 2008. "Locating collection centers for incentive-dependent returns under a pick-up policy with capacitated vehicles," European Journal of Operational Research, Elsevier, vol. 191(3), pages 1223-1240, December.
    7. Wendell, R. E. & McKelvey, R. D., 1981. "New perspectives in competitive location theory," European Journal of Operational Research, Elsevier, vol. 6(2), pages 174-182, February.
    8. 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.
    9. Drezner, Zvi, 1982. "Competitive location strategies for two facilities," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 485-493, November.
    10. 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.
    11. Rhim, Hosun & Ho, Teck H. & Karmarkar, Uday S., 2003. "Competitive location, production, and market selection," European Journal of Operational Research, Elsevier, vol. 149(1), pages 211-228, August.
    12. LEDERER, Philip J. & THISSE, Jacques-François, 1990. "Competitive location on networks under delivered pricing," LIDAM Reprints CORE 893, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. 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.
    14. Zeynep Gümüş & Christodoulos Floudas, 2005. "Global optimization of mixed-integer bilevel programming problems," Computational Management Science, Springer, vol. 2(3), pages 181-212, July.
    15. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    16. Oded Berman & Dmitry Krass, 2002. "Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures," Annals of Operations Research, Springer, vol. 111(1), pages 197-225, March.
    17. Martine Labbé & S. Louis Hakimi, 1991. "Market and Locational Equilibrium for Two Competitors," Operations Research, INFORMS, vol. 39(5), pages 749-756, October.
    18. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    19. Daniel Serra & Charles Revelle, 1993. "Market capture by two competitors: The pre-emptive location problem," Economics Working Papers 39, Department of Economics and Business, Universitat Pompeu Fabra.
    20. Kathrin Fischer, 2002. "Sequential Discrete p-Facility Models for Competitive Location Planning," Annals of Operations Research, Springer, vol. 111(1), pages 253-270, March.
    21. Benati, Stefano & Hansen, Pierre, 2002. "The maximum capture problem with random utilities: Problem formulation and algorithms," European Journal of Operational Research, Elsevier, vol. 143(3), pages 518-530, December.
    22. 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.
    23. Tammy Drezner & Zvi Drezner, 2002. "Validating the Gravity-Based Competitive Location Model Using Inferred Attractiveness," Annals of Operations Research, Springer, vol. 111(1), pages 227-237, March.
    24. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
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