A multiple objective programming approach to linear bilevel multi-follower programming

In this paper, we investigate the relationship between a certain class of linear bilevel multi follower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multi follower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm.