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Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients

Author

Listed:
  • Ali Ebrahimnejad

    (Islamic Azad University, Qaemshahr Branch, Iran)

  • Seyed Hadi Nasseri

    (Mazandaran University, Iran)

  • Sayyed Mehdi Mansourzadeh

    (Islamic Azad University, Jouybar Branch, Iran)

Abstract

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for solving linear programming with fuzzy variables, but their method is not efficient when the decision variables are bounded variables in the auxiliary problem. In this paper the authors introduce an efficient approach to overcome this shortcoming. The bounded fuzzy primal simplex algorithm starts with a primal feasible basis and moves towards attaining primal optimality while maintaining primal feasibility throughout. This algorithm will be useful for sensitivity analysis using primal simplex tableaus.

Suggested Citation

  • Ali Ebrahimnejad & Seyed Hadi Nasseri & Sayyed Mehdi Mansourzadeh, 2011. "Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 2(1), pages 96-120, January.
    • Handle: RePEc:igg:joris0:v:2:y:2011:i:1:p:96-120
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    Cited by:

    1. P. Senthil Kumar, 2018. "Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(2), pages 73-100, April.
    2. 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.
    3. 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.
    4. 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.
    5. P. Senthil Kumar & R. Jahir Hussain, 2016. "A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 7(2), pages 39-61, April.

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