Models and Algorithm for Fuzzy Multi-objective Multi-follower Linear Bilevel Programming

Basic bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his/her objective, subject to a set of constraints and his/her follower´s solution, and the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. Three issues may be involved in a basic bilevel decision problem. One is that bilevel decision making model may involve uncertain parameters which appear either in the objective functions or constraints of the leader or the follower or both. Second, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously. Third, there may have multiple followers in a real decision situation. Following our previous work, this study proposes a set of fuzzy multi-objective multi-follower linear bilevel programming models to describe the three issues. It also develops an approximation branch-and-bound algorithm to solve such kinds of problems.