Journal of Global Optimization

, Volume 38, Issue 4, pp 597–608 | Cite as

Model and extended Kuhn–Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation

  • Jie Lu
  • Chenggen Shi
  • Guangquan Zhang
  • Tharam Dillon
Original Article


When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this bilevel multi-follower issue is where these followers are uncooperatively making their decisions while having cross reference to decision information of the other followers. This situation is called a referential-uncooperative situation in this paper. The well-known Kuhn–Tucker approach has been previously successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this approach to deal with the above-mentioned linear referential-uncooperative bilevel multi-follower decision problem. The paper first presents a decision model for this problem. It then proposes an extended Kuhn–Tucker approach to solve this problem. Finally, a numerical example illustrates the application of the extended Kuhn–Tucker approach.


Bilevel programming Bilevel multi-follower decision Kuhn–Tucker approach Optimization 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Jie Lu
    • 1
  • Chenggen Shi
    • 1
  • Guangquan Zhang
    • 1
  • Tharam Dillon
    • 1
  1. 1.Faculty of Information TechnologyUniversity of TechnologySydneyAustralia

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