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An Extended Branch And Bound Algorithm For Bilevel Multi-Follower Decision Making In A Referential-Uncooperative Situation

Author

Listed:
  • JIE LU

    (Faculty of Information Technology, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

  • CHENGGEN SHI

    (Faculty of Information Technology, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

  • GUANGQUAN ZHANG

    (Faculty of Information Technology, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia)

  • DA RUAN

    (Belgian Nuclear Research Centre (SCK·CEN), Boeretang 200, 2400 Mol, Belgium;
    Department of Applied Mathematics & Computer Science, Ghent University, Krijgslaan 281(S9), 9000 Gent, Belgium)

Abstract

Within the framework of any bilevel decision problem, a leader's decision at the upper level is influenced by the reaction of their follower at the lower level. When multiple followers are involved in a bilevel decision problem, the leader's decision will not only be affected by the reactions of those followers, but also by the relationships among those followers. One of the popular situations within this framework is where these followers are uncooperatively making decisions while having cross reference of decision information, called a referential-uncooperative situation in this paper. The well-known branch and bound algorithm has been successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this algorithm to deal with the above-mentioned linear bilevel multi-follower decision problem by means of a linear referential-uncooperative bilevel multi-follower decision model. It then proposes an extended branch and bound algorithm to solve this problem with a set of illustrative examples in a referential-uncooperative situation.

Suggested Citation

  • Jie Lu & Chenggen Shi & Guangquan Zhang & Da Ruan, 2007. "An Extended Branch And Bound Algorithm For Bilevel Multi-Follower Decision Making In A Referential-Uncooperative Situation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 371-388.
    • Handle: RePEc:wsi:ijitdm:v:06:y:2007:i:02:n:s0219622007002459
    DOI: 10.1142/S0219622007002459
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    References listed on IDEAS

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    1. Jie Lu & Guangquan Zhang & Da Ruan & Fengjie Wu, 2007. "Multi-Objective Group Decision Making:Methods, Software and Applications with Fuzzy Set Techniques(With CD-ROM)," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p505, September.
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    Cited by:

    1. Adejuyigbe O. Fajemisin & Laura Climent & Steven D. Prestwich, 2021. "An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 665-692, September.
    2. Jalali, Mehdi & Zare, Kazem & Seyedi, Heresh, 2017. "Strategic decision-making of distribution network operator with multi-microgrids considering demand response program," Energy, Elsevier, vol. 141(C), pages 1059-1071.
    3. Alipour, Manijeh & Zare, Kazem & Seyedi, Heresh, 2018. "A multi-follower bilevel stochastic programming approach for energy management of combined heat and power micro-grids," Energy, Elsevier, vol. 149(C), pages 135-146.

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