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Efficient solution approaches for a discrete multi-facility competitive interaction model

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  • Robert Aboolian
  • Oded Berman
  • Dmitry Krass

Abstract

In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments show that the approximate approach (with small α) performs extremely well solving large scale problems while the exact approach performs very well for small to medium-sized problems. Copyright Springer Science+Business Media, LLC 2009

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  • 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.
    • Handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:297-306:10.1007/s10479-008-0337-y
    DOI: 10.1007/s10479-008-0337-y
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    References listed on IDEAS

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    1. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
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    3. 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.
    4. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    5. 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.
    6. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
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    Cited by:

    1. 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.
    2. Tammy Drezner & Zvi Drezner & Atsuo Suzuki, 2019. "A cover based competitive facility location model with continuous demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 565-581, October.
    3. Zvi Drezner & Dawit Zerom, 2023. "Competitive facility location under attrition," Computational Management Science, Springer, vol. 20(1), pages 1-19, December.
    4. Laurent Alfandari & Victoire Denoyel & Aurélie Thiele, 2020. "Solving utility-maximization selection problems with Multinomial Logit demand: Is the First-Choice model a good approximation?," Annals of Operations Research, Springer, vol. 292(1), pages 553-573, September.
    5. Godinho, Pedro & Dias, Joana, 2013. "Two-player simultaneous location game: Preferential rights and overbidding," European Journal of Operational Research, Elsevier, vol. 229(3), pages 663-672.

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