Research Article
Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem
Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake,
Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake
Issue:
Volume 11, Issue 5, October 2023
Pages:
77-88
Received:
1 August 2023
Accepted:
21 August 2023
Published:
28 October 2023
Abstract: A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.
Abstract: A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs ma...
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