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A dual simplex method for bounded linear programmes with fuzzy numbers

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  • A. Ebrahimnejad
  • Seyed Hadi Nasseri

Abstract

Fuzzy number linear programming problems have recently attracted some interests. Some authors used the concept of comparison of fuzzy numbers for solving fuzzy linear programming problems. In effect, most convenient methods are based on the concept of comparison of fuzzy numbers by use of ranking functions. But the existing methods are not useful for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, we introduce a new method called the bounded dual simplex method for bounded fuzzy number linear programming problems which is useful for these situations. This algorithm constructs a dual feasible basic solution after obtaining a working basic and from there moves towards attaining primal feasibility while maintaining dual feasibility throughout.

Suggested Citation

  • A. Ebrahimnejad & Seyed Hadi Nasseri, 2010. "A dual simplex method for bounded linear programmes with fuzzy numbers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 2(6), pages 762-779.
    • Handle: RePEc:ids:ijmore:v:2:y:2010:i:6:p:762-779
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    Citations

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    Cited by:

    1. Jagdeep Kaur & Amit Kumar, 2013. "A New Method to Find the Unique Fuzzy Optimal Value of Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 529-534, February.
    2. Diptiranjan Behera, 2024. "Solving epistemic uncertainty based optimization problem with crisp coefficients," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2130-2140, June.
    3. Reza Ghanbari & Khatere Ghorbani-Moghadam & Nezam Mahdavi-Amiri, 2021. "A time variant multi-objective particle swarm optimization algorithm for solving fuzzy number linear programming problems using modified Kerre’s method," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 403-424, June.
    4. S. H. Nasseri & E. Behmanesh, 2013. "Linear programming with triangular fuzzy numbers—A case study in a finance and credit institute," Fuzzy Information and Engineering, Springer, vol. 5(3), pages 295-315, September.
    5. A. Ebrahimenjad, 2011. "A new link between output-oriented BCC model with fuzzy data in the present of undesirable outputs and MOLP," Fuzzy Information and Engineering, Springer, vol. 3(2), pages 113-125, June.
    6. Ali Ebrahimnejad, 2015. "A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 2048-2060, August.
    7. Anila Gupta & Amit Kumar & Mahesh Kumar Sharma, 2013. "Applications of fuzzy linear programming with generalized LR flat fuzzy parameters," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 475-492, December.

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