Linear Bilevel Multifol- Lower Problems"

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Addis Ababa University


With in the framework of any bilevel decision problem, a leader0s decision is in uenced by the reaction of his/her follower(s). When multiple followers who may have had a share in decision variables, objectives and constraints are involved in a bilevel decision problem, the leader0s decision will be afected, not only by the reactions of the followers, but also by the relationships among the followers. This project rst identi es nine di erent kinds of relationships (S1toS9) among the followers. From all these kind, the project mainly focuses on a framework for linear bilevel single follower and linear bilevel multifollower decision problems. For each of the nine relation ships a corresponding linear bilevel single follower and linear bilevel multi-follower decision model are then developed. moreover, this project particularly proposes related theories focusing on an uncooperative decision problem on which decision variables are not totally shared(i.e., S1 model), as this model linear bilevel single follower and linear bilevel multifollower decision problems over the nine kinds of relationships are stated. The solution of such a problem will be in existence if the solution of the lower level problem is uniquely determined and the difculty of solving such a problem is due to the complementarity condition and having many solution of the lower level problem. Two solution procedures i.e., Kuhn-Tucker approach and kth best algorithm are very important to drive an optimal solution for the uncooperative decision model even if they have their own limitations. Keywords: linear bilevel multifollower, kth best algorithm, KKT reformulation, lower level and upper level objective functions and constraints, optimality conditions



Linear Bilevel Multifollower, Kth Best Algorithm, KKT Reformulation, Lower Level and Upper Level Objective Functions and Constraints, Optimality Conditions