IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v64y2016i2d10.1007_s10898-015-0368-2.html

Solving a Huff-like Stackelberg location problem on networks

Author

Listed:
  • Boglárka G.-Tóth

    (Budapest University of Technology and Economics)

  • Kristóf Kovács

    (Budapest University of Technology and Economics)

Abstract

This work deals with a Huff-like Stackelberg problem where the leader wants to locate a facility so that its profit is maximal after the competitor (the follower) has built its facility. We assume that the follower makes a rational decision, maximizing its own profit. The inelastic demand is aggregated into the vertices of a graph, and facilities can be located along the edges. For this computationally hard problem we give a Branch and Bound algorithm using interval analysis and DC bounds. Our computational experience shows that the problem can be solved on medium sized networks in reasonable time.

Suggested Citation

  • Boglárka G.-Tóth & Kristóf Kovács, 2016. "Solving a Huff-like Stackelberg location problem on networks," Journal of Global Optimization, Springer, vol. 64(2), pages 233-247, February.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0368-2
    DOI: 10.1007/s10898-015-0368-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-015-0368-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-015-0368-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. Saidani, Nasreddine & Chu, Feng & Chen, Haoxun, 2012. "Competitive facility location and design with reactions of competitors already in the market," European Journal of Operational Research, Elsevier, vol. 219(1), pages 9-17.
    3. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. Ekaterina Alekseeva & Yury Kochetov & Alexandr Plyasunov, 2015. "An exact method for the discrete $$(r|p)$$ ( r | p ) -centroid problem," Journal of Global Optimization, Springer, vol. 63(3), pages 445-460, November.
    4. Shamekhi Amiri, A. & Torabi, S. Ali & Ghodsi, R., 2018. "An iterative approach for a bi-level competitive supply chain network design problem under foresight competition and variable coverage," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 99-114.
    5. Eligius M. T. Hendrix, 2016. "On competition in a Stackelberg location-design model with deterministic supplier choice," Annals of Operations Research, Springer, vol. 246(1), pages 19-30, November.
    6. Pietro D’Alessandro & Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2024. "The Descent–Ascent Algorithm for DC Programming," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 657-671, March.
    7. Shota Takahashi & Mituhiro Fukuda & Mirai Tanaka, 2022. "New Bregman proximal type algorithms for solving DC optimization problems," Computational Optimization and Applications, Springer, vol. 83(3), pages 893-931, December.
    8. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    9. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    10. Tao Pham Dinh & Yi-Shuai Niu, 2011. "An efficient DC programming approach for portfolio decision with higher moments," Computational Optimization and Applications, Springer, vol. 50(3), pages 525-554, December.
    11. 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.
    12. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    13. 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.
    14. Zhongming Wu & Min Li, 2019. "General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 73(1), pages 129-158, May.
    15. João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.
    16. Chih-Sheng Chuang & Hongjin He & Zhiyuan Zhang, 2022. "A unified Douglas–Rachford algorithm for generalized DC programming," Journal of Global Optimization, Springer, vol. 82(2), pages 331-349, February.
    17. Sinha, Ankur & Malo, Pekka & Deb, Kalyanmoy, 2017. "Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping," European Journal of Operational Research, Elsevier, vol. 257(2), pages 395-411.
    18. Aras Selvi & Aharon Ben-Tal & Ruud Brekelmans & Dick den Hertog, 2022. "Convex Maximization via Adjustable Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2091-2105, July.
    19. F. Mashkoorzadeh & N. Movahedian & S. Nobakhtian, 2022. "The DTC (difference of tangentially convex functions) programming: optimality conditions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 270-295, July.
    20. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0368-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.