IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v316y2022i1d10.1007_s10479-021-04387-4.html
   My bibliography  Save this article

Branch and cut method for solving integer indefinite quadratic bilevel programs

Author

Listed:
  • Nacéra Maachou

    (USTHB)

  • Mustapha Moulaï

    (USTHB)

Abstract

The paper tackles a class of bilevel programming where the upper level problem and the lower level problem are integer indefinite quadratic programs. This article presents a new algorithm for solving the integer indefinite quadratic bilevel problem, say IIQBP. Indeed, the upper level indefinite quadratic problem is solved, the optimal solution of which belongs to the efficient solutions set of the corresponding bicriteria problem. The set of efficient solutions is determined by branch and bound method with cuts. The found integer optimal solution is tested for optimality of the main problem by solving the lower level problem. If this solution is non optimal of IIQBP problem, a cut is added to the upper level problem and a new efficient solutions set is determined then a new integer solution of the upper level problem is found. After the presentation and validation of the algorithm, two examples are provided to better visualize the proposed algorithm.

Suggested Citation

  • Nacéra Maachou & Mustapha Moulaï, 2022. "Branch and cut method for solving integer indefinite quadratic bilevel programs," Annals of Operations Research, Springer, vol. 316(1), pages 197-227, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:1:d:10.1007_s10479-021-04387-4
    DOI: 10.1007/s10479-021-04387-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-021-04387-4
    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/s10479-021-04387-4?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    2. Yasmine Cherfaoui & Mustapha Moulaï, 2021. "Generating the efficient set of MultiObjective Integer Linear plus Linear Fractional Programming Problems," Annals of Operations Research, Springer, vol. 296(1), pages 735-753, January.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    5. C. Bector, 1972. "Indefinite quadratic fractional functional programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 18(1), pages 21-30, December.
    Full references (including those not matched with items on IDEAS)

    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. Sierra-Altamiranda, Alvaro & Charkhgard, Hadi & Eaton, Mitchell & Martin, Julien & Yurek, Simeon & Udell, Bradley J., 2020. "Spatial conservation planning under uncertainty using modern portfolio theory and Nash bargaining solution," Ecological Modelling, Elsevier, vol. 423(C).
    2. Maurizio Zanardi, 2004. "Antidumping law as a collusive device," Canadian Journal of Economics, Canadian Economics Association, vol. 37(1), pages 95-122, February.
    3. M. Hinojosa & A. Mármol & J. Zarzuelo, 2008. "Inequality averse multi-utilitarian bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 597-618, December.
    4. Matsui, Kenji, 2020. "Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain," European Journal of Operational Research, Elsevier, vol. 287(1), pages 225-236.
    5. Simon G�chter & Arno Riedl, "undated". "Moral Property Rights in Bargaining," IEW - Working Papers 113, Institute for Empirical Research in Economics - University of Zurich.
    6. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    7. Erkki Koskela & Ronnie Schöb, 2002. "Alleviating Unemployment: The Case for Green Tax Reforms," Chapters, in: Lawrence H. Goulder (ed.), Environmental Policy Making in Economies with Prior Tax Distortions, chapter 20, pages 355-378, Edward Elgar Publishing.
    8. Magni, Carlo Alberto, 2009. "Splitting up value: A critical review of residual income theories," European Journal of Operational Research, Elsevier, vol. 198(1), pages 1-22, October.
    9. Stefano Vannucci, 2015. "La teoria dei giochi e John Nash," Department of Economics University of Siena 722, Department of Economics, University of Siena.
    10. Roland Kirstein & Matthias Peiss, 2013. "Quantitative Machtkonzepte in der Ökonomik," FEMM Working Papers 130004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    11. Michael Carter & Julian Wright, 1999. "Interconnection in Network Industries," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 14(1), pages 1-25, February.
    12. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    13. Thomas M. Humphrey, 1996. "The early history of the box diagram," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 37-75.
    14. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    15. Izat B. Baybusinov & Enrico Maria Fenoaltea & Yi-Cheng Zhang, 2022. "Negotiation problem," Papers 2201.12619, arXiv.org.
    16. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    17. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
    18. Yan, Ruiliang & Wang, John & Zhou, Bin, 2010. "Channel integration and profit sharing in the dynamics of multi-channel firms," Journal of Retailing and Consumer Services, Elsevier, vol. 17(5), pages 430-440.
    19. S. S. Askar & A. Al-khedhairi, 2019. "Analysis of a Four-Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    20. Marc Fleurbaey, 2000. "Choix social : une difficulté et de multiples possibilités," Revue Économique, Programme National Persée, vol. 51(5), pages 1215-1232.

    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:annopr:v:316:y:2022:i:1:d:10.1007_s10479-021-04387-4. 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.