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Sequential Discrete p-Facility Models for Competitive Location Planning

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  • Kathrin Fischer

Abstract

Two new models for duopolistic competitive discrete location planning with sequential acting and variable delivered prices are introduced. If locations and prices are assumed to be set “once and for all” by the players, the resulting bilevel program is nonlinear. Under the assumption that further price adjustments are possible, i.e., that a Nash equilibrium in prices is reached, the model can be simplified to a linear discrete bilevel formulation. It is shown that in either situation players should not share any locations or markets if they strive for profit-maximization. For the situation with price adjustments, a heuristic solution procedure is suggested. In addition, the bilevel models are shown to serve as a basis from which different well-known location models – as, for example, the p-median problem, the preemptive location problem and the maximum covering problem – can be derived as special cases. Copyright Kluwer Academic Publishers 2002

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  • Kathrin Fischer, 2002. "Sequential Discrete p-Facility Models for Competitive Location Planning," Annals of Operations Research, Springer, vol. 111(1), pages 253-270, March.
    • Handle: RePEc:spr:annopr:v:111:y:2002:i:1:p:253-270:10.1023/a:1020914122189
    DOI: 10.1023/A:1020914122189
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    Citations

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    Cited by:

    1. Xiang Li & Tianyu Zhang & Liang Wang & Hongguang Ma & Xiande Zhao, 2022. "A minimax regret model for the leader–follower facility location problem," Annals of Operations Research, Springer, vol. 309(2), pages 861-882, February.
    2. Vyacheslav Kalashnikov & Vladimir Bulavsky & Vitaliy Kalashnikov & Nataliya Kalashnykova, 2014. "Structure of demand and consistent conjectural variations equilibrium (CCVE) in a mixed oligopoly model," Annals of Operations Research, Springer, vol. 217(1), pages 281-297, June.
    3. Adarsh Kumar Singh & Nachiappan Subramanian & Kulwant Singh Pawar & Ruibin Bai, 2018. "Cold chain configuration design: location-allocation decision-making using coordination, value deterioration, and big data approximation," Annals of Operations Research, Springer, vol. 270(1), pages 433-457, November.
    4. Arbib, Claudio & Pınar, Mustafa Ç. & Tonelli, Matteo, 2020. "Competitive location and pricing on a line with metric transportation costs," European Journal of Operational Research, Elsevier, vol. 282(1), pages 188-200.
    5. Zhang, Yue, 2015. "Designing a retail store network with strategic pricing in a competitive environment," International Journal of Production Economics, Elsevier, vol. 159(C), pages 265-273.
    6. Paveena Chaovalitwongse & Krongsin Somprasonk & Naragain Phumchusri & Joseph Heim & Zelda B. Zabinsky & W. Art Chaovalitwongse, 2017. "A decision support model for staff allocation of mobile medical service," Annals of Operations Research, Springer, vol. 249(1), pages 433-448, February.
    7. Pelegrín, Blas & Fernández, Pascual & Dolores García Pérez, María & Cano Hernández, Saúl, 2012. "On the location of new facilities for chain expansion under delivered pricing," Omega, Elsevier, vol. 40(2), pages 149-158, April.
    8. 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.

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