Skip to main content
SpringerLink
Log in

Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems

  • Original Article
  • Published:
Fuzzy Information and Engineering

Abstract

To the best of our knowledge till now there is no method in the literature to find the exact fuzzy optimal solution of unbalanced fully fuzzy transportation problems. In this paper, the shortcomings and limitations of some of the existing methods for solving the problems are pointed out and to overcome these shortcomings and limitations, two new methods are proposed to find the exact fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as LR flat fuzzy numbers. To show the advantages of the proposed methods over existing methods, a fully fuzzy transportation problem which may not be solved by using any of the existing methods, is solved by using the proposed methods and by comparing the results, obtained by using the existing methods and proposed methods. It is shown that it is better to use proposed methods as compared to existing methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chanas S, Delgado M, Verdegay J L, Vila M A (1993) Interval and fuzzy extension of classical transportation problems. Transportation Planning and Technology 17: 203–218

    Article  Google Scholar 

  2. Chanas S, Kolodziejczyk W, Machaj A A (1984) A fuzzy approach to the transportation problem. Fuzzy Sets and Systems 13: 211–221

    Article  MATH  MathSciNet  Google Scholar 

  3. Chanas S, Kuchta D (1996) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and Systems 82: 299–305

    Article  MathSciNet  Google Scholar 

  4. Chanas S, Kuchta D (1998) Fuzzy integer transportation problem. Fuzzy Sets and Systems 98: 291–298

    Article  MathSciNet  Google Scholar 

  5. Chen M, Ishii H, Wu C, (2008) Transportation problems on a fuzzy network. International Journal of Innovative Computing, Information and Control 4: 1105–1109

    Google Scholar 

  6. Chiang J (2005) The optimal solution of the transportation problem with fuzzy demand and fuzzy product. Journal of Information Science and Engineering 21: 439–451

    MathSciNet  Google Scholar 

  7. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. New York: Academic Press

    MATH  Google Scholar 

  8. Gani A, Razak K A (2006) Two stage fuzzy transportation problem. Journal of Physical Sciences 10: 63–69

    Google Scholar 

  9. Ghatee M, Hashemi S M (2007) Ranking function-based solutions of fully fuzzified minimal cost flow problem. Information Sciences 177: 4271–4294

    Article  MATH  MathSciNet  Google Scholar 

  10. Ghatee M, Hashemi S M (2008) Generalized minimal cost flow problem in fuzzy nature: an application in bus network planning problem. Applied Mathematical Modelling 32: 2490–2508

    Article  MATH  MathSciNet  Google Scholar 

  11. Ghatee M, Hashemi S M (2009) Application of fuzzy minimum cost flow problems to network design under uncertainty. Fuzzy Sets and Systems 160: 3263–3289

    Article  MATH  MathSciNet  Google Scholar 

  12. Ghatee M, Hashemi S M (2009) Optimal network design and storage management in petroleum distribution network under uncertainty. Engineering Applications of Artificial Intelligence 22: 796–807

    Article  Google Scholar 

  13. Ghatee M, Hashemi S M, Hashemi B, Dehghan M (2008) The solution and duality of imprecise network problems. Computers and Mathematics with Applications 55: 2767–2790

    Article  MATH  MathSciNet  Google Scholar 

  14. Ghatee M, Hashemi SM, Zarepisheh M, Khorram E (2009) Preemp-tive priority-based algorithms for fuzzy minimal cost flow problem: an application in hazardous materials transportation. Computers and Industrial Engineering 57: 341–354

    Article  Google Scholar 

  15. Gupta P, Mehlawat M K, (2007) An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit. TOP 15: 114–137

    Article  MATH  MathSciNet  Google Scholar 

  16. Hitchcock F L (1941) The distribution of a product from several sources to numerous localities. Journal of Mathematical Physics 20: 224–230

    MATH  MathSciNet  Google Scholar 

  17. Li L, Huang Z, Da Q, Hu J (2008) A new method based on goal programming for solving transportation problem with fuzzy cost. International Symposiums on Information Processing. 3–8

  18. Lin F T (2009) Solving the transportation problem with fuzzy coefficients using genetic algorithms. IEEE International Conference on Fuzzy Systems. 1468–1473

  19. Liu S T, Kao C (2004) Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research 153: 661–674

    Article  MATH  MathSciNet  Google Scholar 

  20. Liu S T, Kao C (2004) Network flow problems with fuzzy arc lengths. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 34: 765–769

    Article  Google Scholar 

  21. Oheigeartaigh M (1982) A fuzzy transportation algorithm. Fuzzy Sets and Systems 8: 235–243

    Article  MATH  MathSciNet  Google Scholar 

  22. Stephen Dinagar S, Palanivel K (2009) The transportation problem in fuzzy environment. International Journal of Algorithms, Computing and Mathematics 2: 65–71

    Google Scholar 

  23. Yager R R (1981) A procedure for ordering fuzzy subset of the unit subsets of the unit interval. Information Sciences 24: 143–161

    Article  MATH  MathSciNet  Google Scholar 

  24. Zadeh L A (1965) Fuzzy sets. Information and Control 8: 338–353

    Article  MATH  MathSciNet  Google Scholar 

  25. Zimmermann H J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1: 45–55

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147 004, India

    Amit Kumar & Amarpreet Kaur

Authors
  1. Amit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amarpreet Kaur
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Amit Kumar or Amarpreet Kaur.

About this article

Cite this article

Kumar, A., Kaur, A. Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems. Fuzzy Inf. Eng. 3, 81–99 (2011). https://doi.org/10.1007/s12543-011-0068-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12543-011-0068-7

Keywords

Search

Navigation