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A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

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  • Ali Ebrahimnejad

Abstract

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

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  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:11:p:2048-2060
    DOI: 10.1080/00207721.2013.844285
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    References listed on IDEAS

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    1. Saber Saati & Adel Hatami-Marbini & Madjid Tavana & Elham Hajiahkondi, 2012. "A Two-Fold Linear Programming Model with Fuzzy Data," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 2(3), pages 1-12, July.
    2. A. Ebrahimnejad & S.H. Nasseri & F. Hosseinzadeh Lotfi & M. Soltanifar, 2010. "A primal-dual method for linear programming problems with fuzzy variables," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 4(2), pages 189-209.
    3. Liu, Shiang-Tai & Kao, Chiang, 2004. "Solving fuzzy transportation problems based on extension principle," European Journal of Operational Research, Elsevier, vol. 153(3), pages 661-674, March.
    4. 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.
    5. Adel Hatami-Marbini & Madjid Tavana, 2011. "An extension of the linear programming method with fuzzy parameters," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(1), pages 44-55.
    6. SAATI, Saber & HATAMI-MARBINI, Adel & TAVANA, Madjid & HAJIAHKONDI, Elham, 2012. "A two-fold linear programming model with fuzzy data," LIDAM Reprints CORE 2424, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Ali Ebrahimnejad & Jose Luis Verdegay, 2018. "A new approach for solving fully intuitionistic fuzzy transportation problems," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 447-474, December.
    2. Arindam Garai & Palash Mandal & Tapan Kumar Roy, 2016. "Intuitionistic fuzzy T-sets based optimization technique for production-distribution planning in supply chain management," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 950-975, December.

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