Abstract
In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.
Highlights
Bilevel programming is proposed in the literature for dealing with hierarchical systems
Given a bilevel multi-objective programming problems (BMPP), we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP
Given a BMPP, we show how to construct two artificial multi-objective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP
Summary
Bilevel programming is proposed in the literature for dealing with hierarchical systems. F. Bard [4] present results, applications and solution methods for standard formulation where the objective functions and constraints are not necessarily linear. Bard [4] present results, applications and solution methods for standard formulation where the objective functions and constraints are not necessarily linear Despite their multiple applications [5], the special case of bilevel programming problems where each DM has more than one objective function has not yet received a broad attention in the literature.
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