Fuzzy Optimal Solution of Fuzzy Transportation Problems with Transshipments

  • Amit Kumar
  • Amarpreet Kaur
  • Manjot Kaur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6743)

Abstract

In this paper a new method, named as Mehar’s method, is proposed for solving fuzzy transportation problems with transshipments. Also, it is shown that it is better to use Mehar’s method as compared to the existing method.

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References

  1. [1]
    Dantzig, G.B., Thapa, M.N.: Linear programming: 2: theory and extensions. Princeton University Press, New Jersey (1963)CrossRefMATHGoogle Scholar
  2. [2]
    Gani, A., Razak, K.A.: Two stage fuzzy transportation problem. Journal of Physical Sciences 10, 63–69 (2006)Google Scholar
  3. [3]
    Ghatee, M., Hashemi, S.M.: Ranking function-based solutions of fully fuzzified minimal cost flow problem. Information Sciences 177, 4271–4294 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Ghatee, M., Hashemi, S.M.: Generalized minimal cost flow problem in fuzzy nature: An application in bus network planning problem. Applied Mathematical Modelling 32, 2490–2508 (2008)MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Ghatee, M., Hashemi, S.M.: Application of fuzzy minimum cost flow problems to network design under uncertainty. Fuzzy Sets and Systems 160, 3263–3289 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Ghatee, M., Hashemi, S.M.: Optimal network design and storage management in petroleum distribution network under uncertainty. Engineering Applications of Artificial Intelligence 22, 796–807 (2009)CrossRefGoogle Scholar
  7. [7]
    Ghatee, M., Hashemi, S.M., Hashemi, B., Dehghan, M.: The solution and duality of imprecise network problems. Computers and Mathematics with Applications 55, 2767–2790 (2008)MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Ghatee, M., Hashemi, S.M., Zarepisheh, M., Khorram, E.: Preemp-tive priority-based algorithms for fuzzy minimal cost flow problem: An application in hazardous materials transportation. Computers and Industrial Engineering 57, 341–354 (2009)CrossRefGoogle Scholar
  9. [9]
    Gupta, P., Mehlawat, M.K.: An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit. TOP 15, 114–137 (2007)MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Kumar, A., Kaur, A., Gupta, A.: Fuzzy linear programming approach for solving fuzzy transportation problems with transshipment. Journal of Mathematical Modelling and Algorithms (2010), doi: 10.1007/s10852-010-9147-8Google Scholar
  11. [11]
    Li, L., Huang, Z., Da, Q., and Hu, J.: A new method based on goal programming for solving transportation problem with fuzzy cost. In: International Symposiums on Information Processing, 3–8 (2008)Google Scholar
  12. [12]
    Lin, F.T.: Solving the transportation problem with fuzzy coefficients using genetic algorithms. In: IEEE International Conference on Fuzzy Systems, pp. 1468–1473 (2009)Google Scholar
  13. [13]
    Liu, S.T., Kao, C.: Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research 153, 661–674 (2004)MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    Liu, S.T., Kao, C.: Network flow problems with fuzzy arc lengths. IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics 34, 765–769 (2004)CrossRefGoogle Scholar
  15. [15]
    Oheigeartaigh, M.: A fuzzy transportation algorithm. Fuzzy Sets and Systems 8, 235–243 (1982)MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Pandian, P., Natarajan, G.: A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Applied Mathematical Sciences 4, 79–90 (2010)MATHGoogle Scholar
  17. [17]
    Stephen Dinagar, S., Palanivel, K.: The transportation problem in fuzzy environment. International Journal of Algorithms, Computing and Mathematics 2, 65–71 (2009)MATHGoogle Scholar
  18. [18]
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amit Kumar
    • 1
  • Amarpreet Kaur
    • 1
  • Manjot Kaur
    • 1
  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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