Fuzzy Optimal Solution of Interval-Valued Fuzzy Transportation Problems
There are several methods to solve the unbalanced fully fuzzy transportation problems in which the total availability is less than the total demand. In these methods a dummy source, is added to balance the problem. As this added dummy source does not exist actually, it is not genuine to apply existing methods to get real life solutions. So, in this paper a method is proposed to solve such unbalanced transportation problems and the obtained fuzzy optimal solution is in terms of original sources only. By applying the proposed method, we can get the information that the availability of which original source should actually be increased so that the total fuzzy demand is met and the total fuzzy transportation cost is minimum.
KeywordsInterval-valued fuzzy numbers Fully fuzzy transportation problem Fuzzy optimal solution
The first author thanks CSIR, Government of India for providing financial support.
- 2.Taha, H.A.: Operations Research: An Introduction, 8th edn. Prentice-Hall, New Jersey (2007)Google Scholar
- 6.Chiang, J.: The optimal solution of the transportation problem with fuzzy demand and fuzzy product. J. Inf. Sci. Eng. 21, 439–451 (2005)Google Scholar
- 7.Dinagar, D.S., Palanivel, K.: The transportation problem in fuzzy environment. Int. J. Algorithms Comput. Math. 2, 65–71 (2009)Google Scholar
- 11.Yao, J.S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets Syst. 116, 275–288 (2000)Google Scholar