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

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  • Mustafa Sivri
  • Hale Gonce Kocken
  • Inci Albayrak
  • Sema Akin

Abstract

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.

Suggested Citation

  • Mustafa Sivri & Hale Gonce Kocken & Inci Albayrak & Sema Akin, 2019. "Generating a set of compromise solutions of a multi objective linear programming problem through game theory," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(2), pages 77-88.
    • Handle: RePEc:wut:journl:v:2:y:2019:p:77-88:id:1421
    DOI: 10.37190/ord190205
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    References listed on IDEAS

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    1. Cococcioni, Marco & Pappalardo, Massimo & Sergeyev, Yaroslav D., 2018. "Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 298-311.
    2. Sabri, Ehap H. & Beamon, Benita M., 2000. "A multi-objective approach to simultaneous strategic and operational planning in supply chain design," Omega, Elsevier, vol. 28(5), pages 581-598, October.
    3. Das, S. K. & Goswami, A. & Alam, S. S., 1999. "Multiobjective transportation problem with interval cost, source and destination parameters," European Journal of Operational Research, Elsevier, vol. 117(1), pages 100-112, August.
    4. Carlos Romero & Francisco Amador & Antonio Barco, 1987. "Multiple Objectives in Agricultural Planning: A Compromise Programming Application," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 69(1), pages 78-86.
    5. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2005. "Reference point approach for multiple decision makers," European Journal of Operational Research, Elsevier, vol. 164(3), pages 785-791, August.
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