Arithmetic Mean-Based Approach for Solving Fuzzy Multi-Objective Transportation Problems Using Triangular Fuzzy Numbers
Abstract
The transportation problem (TP) is a classical optimization problem in operations research and logistics. The transportation problem is a particular type of Linear Programming Problem (LPP). In the present time scenario, the decision maker handles several objectives simultaneously. This paper presents an approach based on the arithmetic mean technique that solves the Fuzzy Multi-Objective Transportation Problem (FMOTP) in which all the transportation objectives are imprecise and represented by triangular fuzzy numbers. This approach first formulates the given FMOTP into mathematical form and then decomposes it into three levels (lower, middle, and upper) Crisp Multi Objective Transportation Problems (CMOTPs). Then we converted these CMOTPs into Single Objective Transportation Problems (SOTPs) using the Fuzzy Arithmetic Mean (FAM) technique. The combined fuzzy optimal solution is obtained by solving these three SOTPs. TORA software is used to solve these SOTPs. The incentre point is used to defuzzify the fuzzy optimal value to get a crisp optimal value. The proposed approach is elaborated using two numerical examples, and the results are compared with those obtained by other methods.