A New Method For Solving Linear Bilevel Multi-Objective Multi-Follower Programming Problem
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Abstract:
Linear bilevel programming is a decision making problem with a two-level decentralized organization. The leader is in the upper level and the follower, in the lower level. This study addresses linear bilevel multi-objective multi-follower programming (LB-MOMFP) problem, a special case of linear bilevel programming problems with one leader and multiple followers where each decision maker has several objective functions conflicting with each other. We propose a simple and efficient method for solving these problems. In our method, objectives of multi-objective programming problem of the each level decision maker are transformed into fuzzy goals (membership functions) by assigning an aspiration level to each of them, and a max-min decision model is generated for each level problem. Then, we transform obtained linear bilevel multi-follower problem into equivalent single-level problem by extended Karush-Kuhn-Tucker approach. Finally, numerical examples are given to demonstrate the feasibility and efficiency of the proposed method. This paper aims to present a simple technique to obtain better compromise solution of LB-MOMFP problem than earlier techniques. A comparative analysis based on numerical examples is carried out to show preference of the proposed method
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Journal title
volume 6 issue None
pages 13- 26
publication date 2016-11
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