A new approach to solving multi-follower multi-objective linear bilevel programming problems

Journal of Optimization in Industrial Engineering

مقاله 1، دوره 16، شماره 1 - شماره پیاپی 34، شهریور 2023، صفحه 1-7   

نوع مقاله: Original Manuscript

شناسه دیجیتال (DOI): 10.22094/joie.2022.543647.1512

نویسندگان

Habibe Sadeghi^{* 1}؛ Farzaneh Anis Hosseini²

¹Faculty of mathematical science and computer, shahid chamran university of ahvaz, Ahvaz, Iran

²Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

چکیده

In this paper, we present a suitable extension of the approach described by Pieume et al. (2011) for solving multi-follower multi-objective linear bilevel programming problems. This problem is a special case of multi-follower bilevel linear programming problems, where each decision maker possesses several objective functions that in some cases, conflict with one another. We construct a multi-objective linear programming problem. Furthermore, we show that the multi-follower multi-objective linear bilevel programming problem can be reduced to optimize the top-level multi-objective linear programming problem over an efficient set. The proposed approach uses a Pareto-filter scheme, and obtains an approximate discrete representation efficient set unlike the fuzzy approaches that only obtain one efficient solution.  Ultimately, a numerical example is presented to illustrate the efficiency of the proposed approach.

کلیدواژه‌ها

Multi-objective programming؛ Multi-follower linear bilevel programming؛ Pareto-optimal solutions؛ Feasible set

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