Fuzzy Transportation Problem through Monalisha’s Approximation Method
S. Vimala
Department of Mathematics, Mother Teresa Women’s University, Kodaikannal, Tamilnadu, India.
S. Krishna Prabha *
Mother Teresa Women’s University, Kodaikannal, India and Department of Mathematics, PSNA CET, Dindigul, Tamilnadu, India.
*Author to whom correspondence should be addressed.
Abstract
Transportation Problem (TP) is based on supply and demand of commodities transported from several sources to the different destinations. Usual methods for calculating initial basic feasible solution are North-West corner method, least cost method, row minima method/ column minima method, Russell’s method, Vogel’s approximation method etc. The transportation costs are considered as imprecise numbers described by fuzzy numbers which are more realistic and general in nature. Since the objective is to minimize the total cost or to maximize the total profit, subject to some fuzzy constraints, the objective function is also considered as a fuzzy number. The method is to rank the fuzzy objective values of the objective function by some ranking method to find the best alternative. On the basis of this idea method of magnitude ranking technique has been adopted to transform the fuzzy transportation problem and the initial basic feasible solution is found by Monalisha's Approximation Method (MAM'S).
An numerical illustration is also discussed.
Keywords: Triangular fuzzy numbers, method of magnitude ranking technique, fuzzy transportation problem.