Methods for solving unbalanced fuzzy transportation problems
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.
KeywordsFuzzy 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).
- Dantzig GB, Thapa MN (1963) Linear programming: 2: theory and extensio- ns. Princeton University Press, New JerseyGoogle Scholar
- Dinagar DS, Palanivel K (2009) The transportation problem in fuzzy environ- ment. Int J Algorithms Comput Math 2:65–71Google Scholar
- Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New YorkGoogle Scholar
- Gani A, Razak KA (2006) Two stage fuzzy transportation problem. J Phys Sci 10:63–69Google Scholar
- Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230Google Scholar
- Pandian P, Natarajan G (2010) A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Appl Math Sci 4:79–90Google Scholar
- Saad OM, Abbas SA (2003) A parametric study on transportation problem under fuzzy environment. J Fuzzy Math 11:115–124Google Scholar