Fuzzy Information and Engineering

, Volume 3, Issue 1, pp 81–99 | Cite as

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

Original Article


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.


Fuzzy transportation problem Ranking function LR flat fuzzy number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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: 203–218CrossRefGoogle Scholar
  2. 2.
    Chanas S, Kolodziejczyk W, Machaj A A (1984) A fuzzy approach to the transportation problem. Fuzzy Sets and Systems 13: 211–221CrossRefMATHMathSciNetGoogle Scholar
  3. 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: 299–305CrossRefMathSciNetGoogle Scholar
  4. 4.
    Chanas S, Kuchta D (1998) Fuzzy integer transportation problem. Fuzzy Sets and Systems 98: 291–298CrossRefMathSciNetGoogle Scholar
  5. 5.
    Chen M, Ishii H, Wu C, (2008) Transportation problems on a fuzzy network. International Journal of Innovative Computing, Information and Control 4: 1105–1109Google Scholar
  6. 6.
    Chiang J (2005) The optimal solution of the transportation problem with fuzzy demand and fuzzy product. Journal of Information Science and Engineering 21: 439–451MathSciNetGoogle Scholar
  7. 7.
    Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. New York: Academic PressMATHGoogle Scholar
  8. 8.
    Gani A, Razak K A (2006) Two stage fuzzy transportation problem. Journal of Physical Sciences 10: 63–69Google Scholar
  9. 9.
    Ghatee M, Hashemi S M (2007) Ranking function-based solutions of fully fuzzified minimal cost flow problem. Information Sciences 177: 4271–4294CrossRefMATHMathSciNetGoogle Scholar
  10. 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: 2490–2508CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Ghatee M, Hashemi S M (2009) Application of fuzzy minimum cost flow problems to network design under uncertainty. Fuzzy Sets and Systems 160: 3263–3289CrossRefMATHMathSciNetGoogle Scholar
  12. 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: 796–807CrossRefGoogle Scholar
  13. 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: 2767–2790CrossRefMATHMathSciNetGoogle Scholar
  14. 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: 341–354CrossRefGoogle Scholar
  15. 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: 114–137CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Hitchcock F L (1941) The distribution of a product from several sources to numerous localities. Journal of Mathematical Physics 20: 224–230MATHMathSciNetGoogle Scholar
  17. 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. 3–8Google Scholar
  18. 18.
    Lin F T (2009) Solving the transportation problem with fuzzy coefficients using genetic algorithms. IEEE International Conference on Fuzzy Systems. 1468–1473Google Scholar
  19. 19.
    Liu S T, Kao C (2004) Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research 153: 661–674CrossRefMATHMathSciNetGoogle Scholar
  20. 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: 765–769CrossRefGoogle Scholar
  21. 21.
    Oheigeartaigh M (1982) A fuzzy transportation algorithm. Fuzzy Sets and Systems 8: 235–243CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Stephen Dinagar S, Palanivel K (2009) The transportation problem in fuzzy environment. International Journal of Algorithms, Computing and Mathematics 2: 65–71Google Scholar
  23. 23.
    Yager R R (1981) A procedure for ordering fuzzy subset of the unit subsets of the unit interval. Information Sciences 24: 143–161CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Zadeh L A (1965) Fuzzy sets. Information and Control 8: 338–353CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Zimmermann H J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1: 45–55CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2011

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

Personalised recommendations