Operational Research

, Volume 12, Issue 3, pp 287–316 | Cite as

Methods for solving unbalanced fuzzy transportation problems

Original Paper


In this paper, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems occurring in real life situations. Also, a new representation of trapezoidal fuzzy numbers is proposed. The advantages of the proposed methods over existing methods and the proposed representation of trapezoidal fuzzy numbers over existing representation are also discussed. To illustrate the proposed methods an unbalanced fuzzy transportation problem is solved by using both the proposed methods and it is shown that the obtained results are same.


Fuzzy transportation problem Ranking function Trapezoidal fuzzy number JMD trapezoidal fuzzy number 



The authors would like to thank to the Editor-in-Chief “Professor Constantin Zopounidis” and the anonymous reviewers for their suggestions which have led to an improvement in both the quality and clarity of the paper. Dr. Amit Kumar want to acknowledge the adolescent inner blessings of Mehar without which it was not possible to think the idea proposed in this manuscript. Mehar is a lovely daughter of Parmpreet Kaur (Research scholar under the supervision of Dr. Amit Kumar).


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia

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