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

• Autorzy: Sivri Mustafa , Kocken Hale Gonce , Albayrak Inci , Akin Sema

Identyfikatory

DOI

10.5277/ord190205

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multi-objective programming problem; game theory; compromise solution

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2019
• Tom: Vol. 29, No. 2
• Strony: 77--88
• Opis fizyczny: Bibliogr.27 poz., tab.

Twórcy

autor

Sivri Mustafa

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

autor

Kocken Hale Gonce

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

autor

Albayrak Inci

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

autor

Akin Sema

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

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).