Abstract
The relationship between the reference-uncooperative linear bilevel two-follower decision making and the multi-objective decision making has been recently considered (Sadeghi and Moslemi, 2019). In this paper, we address the foregoing relation for the
 uncooperative linear bilevel multi-follower programming (ULBMFP) model with followers. Furthermore, we consider some geometric properties of the feasible solutions set of the ULBMFP problem. Moreover an algorithm to find an optimal solution for the ULBMFP problem was proposed. Ultimately, some numerical examples to illustrate the proposed algorithm were provided.
Highlights
Multilevel programming (MLP) problem is developed to deal with the decentralized decision-making situations in which decision-makers are arranged within a hierarchical structure
In Glackin et al (2009), two algorithms based on the multi-objective linear programming (MOLP) techniques to solve the linear bilevel programming (LBLP) problems were presented
We have investigated the relationship between the uncooperative linear bilevel multi-follower programming (ULBMFP) problems and the MOLP problems
Summary
Multilevel programming (MLP) problem is developed to deal with the decentralized decision-making situations in which decision-makers are arranged within a hierarchical structure. The BLP problem may involve multiple decision-makers at the lower level, and these followers may have different reactions to a possible decision by the leader In this case, the BLP problem is called a bilevel multi-follower programming (BLMFP) problem. We consider a class of linear BLMFP problems wherein each follower controls a separate set of decision variables and attempts to optimize its own objective function over its own constraints It is called an uncooperative linear bilevel multi-follower programming (ULBMFP) problem (Zhang et al, 2016). We discuss some geometric properties of the feasible solutions set of the ULBMFP problem in special cases
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