IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v164y2015i2d10.1007_s10957-014-0579-6.html
   My bibliography  Save this article

Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions

Author

Listed:
  • Dalbinder Kaur

    (National Institute of Technology)

  • Sathi Mukherjee

    (Bengal College of Engineering and Technology)

  • Kajla Basu

    (National Institute of Technology)

Abstract

The paper presents the application of an exponential membership function to fuzzy programming technique for solving a multi-objective and multi-index real-life transportation problem. It focusses on the minimization of the transportation cost, deterioration rate and underused capacity of the transported raw materials like coal, iron ore, etc. from different sources to different destination sites at Durgapur Steel Plant, Durgapur, West Bengal, India, by different transportation modes like train, trucks, etc. A special type of non-linear (exponential) membership function is assigned to each objective function. Thus, the paper presents fuzzy programming approach with an exponential function to a real-life transportation problem and develops a non-dominated compromise solution. In addition, the interval-valued numbers used in supply and demand parameters represent the uncertainties in a real-life problems. The optimization models have a wide use in real-life multi-objective transportation problems. The use of fuzzy programming technique has been successfully concluded for the focussed transportation problem taking a linear and a hyperbolic membership function. But the numerical illustration shows that exponential membership function gives a better and comparable result for the problem.

Suggested Citation

  • Dalbinder Kaur & Sathi Mukherjee & Kajla Basu, 2015. "Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 666-678, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0579-6
    DOI: 10.1007/s10957-014-0579-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0579-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-014-0579-6?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. Tzeng, Gwo-Hshiung & Teodorovic, Dusan & Hwang, Ming-Jiu, 1996. "Fuzzy bicriteria multi-index transportation problems for coal allocation planning of Taipower," European Journal of Operational Research, Elsevier, vol. 95(1), pages 62-72, November.
    2. Junginger, Werner, 1993. "On representatives of multi-index transportation problems," European Journal of Operational Research, Elsevier, vol. 66(3), pages 353-371, May.
    3. Das, S. K. & Goswami, A. & Alam, S. S., 1999. "Multiobjective transportation problem with interval cost, source and destination parameters," European Journal of Operational Research, Elsevier, vol. 117(1), pages 100-112, August.
    4. Anoop Kumar Dhingra & Moskowitz, Herbert, 1991. "Application of fuzzy theories to multiple objective decision making in system design," European Journal of Operational Research, Elsevier, vol. 53(3), pages 348-361, August.
    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. Abd Elazeem M. Abd Elazeem & Abd Allah A. Mousa & Mohammed A. El-Shorbagy & Sayed K. Elagan & Yousria Abo-Elnaga, 2021. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems," Sustainability, MDPI, vol. 13(3), pages 1-18, January.
    2. Dalbinder Kour & Sathi Mukherjee & Kajla Basu, 2017. "Solving intuitionistic fuzzy transportation problem using linear programming," 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. 8(2), pages 1090-1101, November.
    3. Deepika Rani & T. R. Gulati, 2016. "Application of intuitionistic fuzzy optimization technique in transportation models," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 761-777, 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. Kravtsov, M.K. & Lukshin, E.V., 2008. "Polyhedral combinatorics of multi-index axial transportation problems," European Journal of Operational Research, Elsevier, vol. 189(3), pages 920-938, September.
    2. Sumati Mahajan & S. K. Gupta, 2021. "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Annals of Operations Research, Springer, vol. 296(1), pages 211-241, January.
    3. Pérez-Mesa, Juan Carlos & Galdeano-Gómez, Emilio & Salinas Andújar, Jose A., 2012. "Logistics network and externalities for short sea transport: An analysis of horticultural exports from southeast Spain," Transport Policy, Elsevier, vol. 24(C), pages 188-198.
    4. Woo, Hong Seng & Saghiri, Soroosh, 2011. "Order assignment considering buyer, third-party logistics provider, and suppliers," International Journal of Production Economics, Elsevier, vol. 130(2), pages 144-152, April.
    5. Sadeghi, Mehdi & Mirshojaeian Hosseini, Hossein, 2006. "Energy supply planning in Iran by using fuzzy linear programming approach (regarding uncertainties of investment costs)," Energy Policy, Elsevier, vol. 34(9), pages 993-1003, June.
    6. S. K. Bharati & Rita Malhotra, 2017. "Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle," 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. 8(2), pages 1442-1449, November.
    7. 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.
    8. Teodorovic, Dus[caron]an, 1999. "Fuzzy logic systems for transportation engineering: the state of the art," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(5), pages 337-364, June.
    9. Kim, Kwang-Jae & Moskowitz, Herbert & Dhingra, Anoop & Evans, Gerald, 2000. "Fuzzy multicriteria models for quality function deployment," European Journal of Operational Research, Elsevier, vol. 121(3), pages 504-518, March.
    10. Deepika Rani & T. R. Gulati, 2016. "Application of intuitionistic fuzzy optimization technique in transportation models," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 761-777, December.
    11. 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.
    12. Dhingra, A. K. & Rao, S. S., 1995. "A cooperative fuzzy game theoretic approach to multiple objective design optimization," European Journal of Operational Research, Elsevier, vol. 83(3), pages 547-567, June.
    13. Drexl, Andreas & Salewski, Frank, 1997. "Distribution requirements and compactness constraints in school timetabling," European Journal of Operational Research, Elsevier, vol. 102(1), pages 193-214, October.
    14. Chan, Felix T. S. & Chung, S. H. & Wadhwa, Subhash, 2005. "A hybrid genetic algorithm for production and distribution," Omega, Elsevier, vol. 33(4), pages 345-355, August.
    15. Abd Elazeem M. Abd Elazeem & Abd Allah A. Mousa & Mohammed A. El-Shorbagy & Sayed K. Elagan & Yousria Abo-Elnaga, 2021. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems," Sustainability, MDPI, vol. 13(3), pages 1-18, January.
    16. Sujeet Kumar Singh & Shiv Prasad Yadav, 2018. "Intuitionistic fuzzy multi-objective linear programming problem with various membership functions," Annals of Operations Research, Springer, vol. 269(1), pages 693-707, October.
    17. Tzeng, Gwo-Hshiung & Teodorovic, Dusan & Hwang, Ming-Jiu, 1996. "Fuzzy bicriteria multi-index transportation problems for coal allocation planning of Taipower," European Journal of Operational Research, Elsevier, vol. 95(1), pages 62-72, November.
    18. Xie, Fanrong & Butt, Muhammad Munir & Li, Zuoan & Zhu, Linzhi, 2017. "An upper bound on the minimal total cost of the transportation problem with varying demands and supplies," Omega, Elsevier, vol. 68(C), pages 105-118.
    19. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    20. Jafar Rezaei & Negin Salimi, 2015. "Optimal ABC inventory classification using interval programming," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 1944-1952, August.

    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:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0579-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.