A New Efficient Method to Solve Bi-Objective Transportation Problems Under Fuzzy Parameters

The transportation problem (TP) is a classical optimization problem in operations research and logistics. Due to several factors, real-life situations may have inconsistent supply, demand, and unit transportation costs. The fuzzy numbers represent these inaccurate data. In the present scenario, the decision-maker handles several objectives simultaneously. This paper presents a simple method to solve linear Bi-Objective Transportation Problems (BOTP) using (η, ξ) interval-valued fuzzy numbers (IVFN), offering a more realistic way to model uncertainty than normal fuzzy numbers. Using the signed distance ranking, the Fuzzy BOTP was transformed into the equivalent crisp BOTP. In this paper, A method is developed based on assigning the allocation in the objective's minimum cost, corresponding to the row and column cells with the minimum objective value. A unique, efficient solution is obtained directly, leading to an optimal compromise solution that the decision-maker prefers using the proposed method. The proposed method aims to assign the allocation in a way that minimizes the total objective value. The compromise (η, ξ) fuzzy efficient solution as well as the crisp efficient solution of the fuzzy BOTP is provided by this method, which has a minimum distance from the ideal solution. This proposed method is less time-consuming and simple to use. A numerical example is used to illustrate our proposed method and to compare the results with some other existing methods. The proposed method provides a non-degenerate efficient compromise solution for the example, which has a minimum distance (33.95) from the ideal solution.