Generating a set of compromise solutions of a multi objective linear programming problem through game theory.

• Authors: SİVRİ Mustafa , KOCKEN Hale Gonce , ALBAYRAK Inci , AKİN Sema
• Languages of publication: EN

Abstracts

Most of real-life problems, including design, optimization, scheduling and control, etc., are inherently characterized by multiple conflicting objectives, and thus multi-objective linear programming (MOLP) problems are frequently encountered in the literature. One of the biggest difficulties in solving MOLP problems lies in the trade-off among objectives. Since the optimal solution of one objective may lead other objective(s) to bad results, all objectives must be optimized simultaneously. Additionally, the obtained solution will not satisfy all the objectives in the same satisfaction degree. Thus, it will be useful to generate a set of compromise solutions in order to present it to the decision maker (DM). With this motivation, after determining a modified payoff matrix for MOLP, all possible ratios are formed between all rows. These ratio matrices are considered a two person zero-sum game and solved by linear programming (LP) approach. Taking into consideration the results of the related game, the original MOLP problem is converted to a single objective LP problem. Since there exist numerous ratio matrices, a set of compromise solutions is obtained for MOLP problem. Numerical examples are used to demonstrate this approach.

Keywords

EN

multi-objective programming problem; game theory; compromise solution

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2019
• Volume: 29
• Issue: 2
• Pages: 77-88

Contributors

author

SİVRİ Mustafa

• Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey

author

KOCKEN Hale Gonce

• Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey

author

ALBAYRAK Inci

• Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey,

author

AKİN Sema

• Department of Mathematics, Yildiz Technical University, Davutpasa, 34220 Esenler/Istanbul, Turkey

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Identifiers

DOI

10.5277/ord190205