An Efficient Algorithm to Obtain the Optimal Solution for Fuzzy Transportation Problems International Journal of Computer & Organization Trends (IJCOT) © 2014 by IJCOT Journal Volume - 4 Issue - 1 Year of Publication : 2014 Authors : S.Krishna Prabha , S.Devi , S.Deepa 10.14445/22492593/IJCOT-V4P309 S.Krishna Prabha , S.Devi , S.Deepa, "An Efficient Algorithm to Obtain the Optimal Solution for Fuzzy Transportation Problems", International Journal of Computer & organization Trends  (IJCOT), V4(1):17-21 Jan - Feb 2014, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract—In this paper we solve the Fuzzy Transportation problems by using a new algorithm namely EAVAM . We introduce an approach for solving a wide range of such problems by using a method which applies it for ranking of the fuzzy numbers. Some of the quantities in a fuzzy transportation problem may be fuzzy or crisp quantities. In many fuzzy decision problems, the quantities are represented in terms of fuzzy numbers. Fuzzy numbers may be normal or abnormal, triangular or trapezoidal or any LR fuzzy number. Thus, some fuzzy numbers are not directly comparable. First, we transform the fuzzy quantities as the cost, coefficients, supply and demands, into crisp quantities by using our method and then by using the EAVAM, we solve and obtain the solution of the problem. The new method is systematic procedure, easy to apply and can be utilized for all types of transportation problem whether maximize or minimize objective function. Finally we explain this method with a numerical example.

References

 A. Nagoor Gani and K. Abdul Razak, Two stage fuzzy transportation problem, European Journal of Operational Research, 153(2004), 661-674.
 C. H. Cheng, A new approach for ranking fuzzy numbers by distance method, fuzzy sets and systems, 95 (1998) 307-317.
 H. Basirzadeh, R. Abbasi, A new approach for ranking fuzzy numbers based on α−cuts, JAMI, Journal of Appied Mathematics & Informatic,26(2008) 767-778.
 H. Basirzadeh, R. Abbasi, An Approach for solving fuzzy Transportation problems, Applied Mathematical Sciences, Vol. 5, 2011, no. 32, 1549 - 1566
 H. J. Zimmermann, Fuzzy set theory and its Applications, second edition,kluwer Academic, Boston, 1996.
 H. W. Lu, C. B. Wang, An Index for ranking fuzzy numbers by belieffeature, Information and management science, 16(3) (2005) 57-70.
 M. Detyniecki, R. R. Yager, Ranking fuzzy numbers using α−weightedValuations, International Journal of uncertainty, Fuzziness and knowledge-Based systems, 8(5) (2001) 573-592.
 M. S. Bazarra, John J. Jarvis, Hanif D. Sherali, Linear programming and network flows, (2005).
 M. Shanmugasundari, K. Ganesan , A Novel Approach for the fuzzy optimal solution of Fuzzy Transportation Problem, International Journal of Engineering Research and Applications (IJERA) Vol. 3, Issue 1, January -February 2013, pp.1416-1424
 P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers,fuzzy sets and systems, 153 (2005) 115-135.
 P. Pandian and G. Natarajan, A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems, Applied Mathematical Sciences, 4(2010), 79-90.
 S. Abbasbandy, B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Applied mathematics and computation, 159 (2004) 381-386.
 S. Abbasbandy, B. Asady, Ranking of fuzzy numbers by sign distance,Information science, 176 (2006) 2405-2416.
 S. Chanas and D. Kuchta, A concept of the optimal solution of the transportation problem with fuzzy cost coefficients, , Fuzzy sets and Systems,82 (1996) 299-305.
 S. Chanas, W. Kolodziejczyk and A. Machaj, A fuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13 (1984) 211-221.
 Shiang-Tai Liu and Chiang Kao, Solving fuzzy transportation problems based on extension principle, Journal of Physical Science, 10(2006), 63-69.
 T. C. Chu, C. T. Tsao, Ranking fuzzy numbers with an area between the centroid point and original point, compute. math. Appl., 43 (2002) 111-117.

Keywords
Optimization, Transportation problem, ranking of fuzzy numbers, Fuzzy sets, Fuzzy transportation problem.