IAETSD JOURNAL FOR ADVANCED RESEARCH IN APPLIED SCIENCES ISSN NO: 2394-8442
ATM for solving fuzzy transportation problem using method of magnitude S.Krishna Prabha #1, S.Vimala *2 Ph.D Scholar, Mother Teresa Women’s University, Kodaikannal Assistant Professor ,PSNA CET, Dindigul *Assistant Professor, Mother Teresa Women’s University, Kodaikannal #
1
[email protected] 2
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Abstract: In this paper, we use allocation table method (ATM) for solving fuzzy transportation problem (FTP) using method of magnitude ranking for the representative value of the fuzzy number. This paper justifies the efficiency of Allocation Table Method for solving maximization transportation problems. Moreover, this method is illustrated with numerical examples. In this process, it is pragmatic that the Allocation Table Method (ATM) is a well-organized process for solving transportation maximization problems. Keywords— Trapezoidal Fuzzy Numbers, Method of Magnitude Ranking Technique, Fuzzy transportation problem
I. INTRODUCTION Transportation models present a strong arrangement to meet up the confront of how to supply the merchandise to the customers in more proficient ways. They guarantee the competentprogress and sensibleaccessibility of raw materials and completed goods.The essential transportation problem was, at first developed by Hitchcock [2] in 1941. Charnes et al[5] in 1953 proposed the stepping stone technique which provided an different way of shaping the simplex method. Dantzig [6] in 1963 developed the primal simplex transportation method. Numerous researchers deliberatedbroadly to solve cost minimizing transportation problem in differentmethods. In existent applications, all the parameters of the transportation problems may not be known specificallyowing to unmanageable factors. This sort of vagueinformation is not always well represented by random variable chosen from a probability distribution. To indicate this data fuzzy numbers are introduced by Zadeh in 1965[17]. Zimmermannin1978 [3] proposed that the solutions obtained by fuzzy linear programming are always proficient. Saad & Abbas in 2003 [24] developed an algorithm for finding the solution for the transportation problems in fuzzy environment. A new algorithm, specificallycalled as fuzzy zero point method was projected by Pandian & Natrajan in 2010, [18, 19, 20]. Sobha in 2014 [25] proposed a new method for solving unbalanced transportation problems. Hajjari & Abbasbandy in 2011 projected a promoter operator for defuzzification Methods with method of magnitude. Mollah Mesbahuddin Ahmed et al(2016) have proposed Incessant Allocation Method for Solving Transportation Problems. Md Sharif Uddin et al(2016) have provided the Allocation Table Method For Solving Transportation Maximization Problems. Darunee Hunwisaiand Poom Kumam (2017) solved a fuzzy transportation problem via Robust ranking technique and ATM. In this paper a balanced fuzzy transportation problem, is defuzzified by using method of magnitude technique and Allocation Table Method (ATM) is applied. Some basic concepts and operations of fuzzy set theory and Method of magnitude, for ranking fuzzy numbers have been proposed in section 2. In section 3, corresponding algorithm called Allocation Table Method (ATM)
VOLUME 5, ISSUE 3, MAR/2018
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IAETSD JOURNAL FOR ADVANCED RESEARCH IN APPLIED SCIENCES ISSN NO: 2394-8442 have been introduced for Fuzzy Transportation Problem. In Section 4 a numerical example has been illustrated. Conclusion is given in section 5. II PRELIMINARIES TRAPEZOIDAL AND TRIANGULAR FUZZY NUMBERS If the membership function
is piecewise linear, Then
is said to be a trapezoidal fuzzy number. The membership
function of a trapezoidal fuzzy number is given by
If w = 1, then = (a, b, c, d; 1) is a normalized trapezoidalfuzzy number and number if 0 < w
