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Robust optimality analysis of non-degenerate basic feasible solutions in linear programming problems with fuzzy objective coefficients

Author

Listed:
  • Masahiro Inuiguchi

    (Osaka University)

  • Zhenzhong Gao

    (Osaka University)

  • Carla Oliveira Henriques

    (Coimbra Business School Research Centre—ISCAC
    University of Coimbra
    University of Coimbra, CeBER)

Abstract

The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods.

Suggested Citation

  • Masahiro Inuiguchi & Zhenzhong Gao & Carla Oliveira Henriques, 2023. "Robust optimality analysis of non-degenerate basic feasible solutions in linear programming problems with fuzzy objective coefficients," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 51-79, March.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:1:d:10.1007_s10700-022-09383-2
    DOI: 10.1007/s10700-022-09383-2
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    References listed on IDEAS

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    1. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.
    2. Richard E. Wendell, 1985. "The Tolerance Approach to Sensitivity Analysis in Linear Programming," Management Science, INFORMS, vol. 31(5), pages 564-578, May.
    3. H E Mausser & M Laguna, 1999. "Minimising the maximum relative regret for linear programmes with interval objective function coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1063-1070, October.
    4. Filippi, Carlo, 2005. "A fresh view on the tolerance approach to sensitivity analysis in linear programming," European Journal of Operational Research, Elsevier, vol. 167(1), pages 1-19, November.
    5. S. Rivaz & M. Yaghoobi, 2013. "Minimax regret solution to multiobjective linear programming problems with interval objective functions coefficients," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 625-649, September.
    6. Inuiguchi, Masahiro & Sakawa, Masatoshi, 1995. "Minimax regret solution to linear programming problems with an interval objective function," European Journal of Operational Research, Elsevier, vol. 86(3), pages 526-536, November.
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