IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v46y2015i11p2048-2060.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2013.844285
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2013.844285?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. P. Senthil Kumar, 2016. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 5(4), pages 121-146, October.
    2. P. Senthil Kumar, 2018. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(1), pages 102-129.
    3. 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.
    4. 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.
    5. S. Dutta & S. Acharya & Rajashree Mishra, 2016. "Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 835-872, December.
    6. Bogdana Stanojević & Milan Stanojević & Sorin Nădăban, 2021. "Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    7. Jung-Lin Hung & Cheng-Che Chen & Chun-Mei Lai, 2020. "Possibility Measure of Accepting Statistical Hypothesis," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    8. Manuel Arana-Jiménez & Carmen Sánchez-Gil, 2020. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers," Journal of Global Optimization, Springer, vol. 77(1), pages 27-52, May.
    9. Dayi He & Ran Li & Qi Huang & Ping Lei, 2014. "Transportation Optimization with Fuzzy Trapezoidal Numbers Based on Possibility Theory," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-12, August.
    10. Peidro, David & Mula, Josefa & Jiménez, Mariano & del Mar Botella, Ma, 2010. "A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment," European Journal of Operational Research, Elsevier, vol. 205(1), pages 65-80, August.
    11. Sharma, Dinesh K. & Jana, R.K., 2009. "A hybrid genetic algorithm model for transshipment management decisions," International Journal of Production Economics, Elsevier, vol. 122(2), pages 703-713, December.
    12. Mohammed, Ahmed & Wang, Qian, 2017. "The fuzzy multi-objective distribution planner for a green meat supply chain," International Journal of Production Economics, Elsevier, vol. 184(C), pages 47-58.
    13. Chia-Nan Wang & Thanh-Tuan Dang & Tran Quynh Le & Panitan Kewcharoenwong, 2020. "Transportation Optimization Models for Intermodal Networks with Fuzzy Node Capacity, Detour Factor, and Vehicle Utilization Constraints," Mathematics, MDPI, vol. 8(12), pages 1-27, November.
    14. 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.
    15. 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.
    16. Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    17. Jiuping Xu & Guomin Fang & Zezhong Wu, 2016. "Network equilibrium of production, transportation and pricing for multi-product multi-market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 567-595, December.
    18. Amit Kumar & Amarpreet Kaur, 2011. "Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems," Fuzzy Information and Engineering, Springer, vol. 3(1), pages 81-99, March.
    19. Zhao, Jing & Tang, Wansheng & Zhao, Ruiqing & Wei, Jie, 2012. "Pricing decisions for substitutable products with a common retailer in fuzzy environments," European Journal of Operational Research, Elsevier, vol. 216(2), pages 409-419.
    20. Wong, Bo K. & Lai, Vincent S., 2011. "A survey of the application of fuzzy set theory in production and operations management: 1998-2009," International Journal of Production Economics, Elsevier, vol. 129(1), pages 157-168, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:tsysxx:v:46:y:2015:i:11:p:2048-2060. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.