The Multi-Objective Transportation Problem Solve with Geometric Mean and Penalty Methods

Abstract

The traditional (classical) Transportation Problem (TP) can be viewed as a specific case of the Linear Programming (LP) problem, as well as its models are used to find the best solution for the problem of predetermined how many units of a good or service need to be shipped from one source to multiple locations, with the goals being to reduce time or expense. Classical TP has one objective but when there are two or more objectives to be optimized for in a TP, the strategies used to optimize a single objective are inapplicable. The term “Multi-Objective Transportation Problem (MOTP)” refers to situations in which there are two or more objectives in a TP. The specific extension of the transportation problem is the MOTP. This work provided a novel alternative algorithm that uses geometric means along with the penalty technique to address MOTP. Specifically, analyzed data by comparing our method with numerical examples and presenting the results in a line graph. Our analysis shows that our approach yields better solutions than existing methods, demonstrating the novelty and effectiveness of our approach. The comparison with numerical examples provides a clear and intuitive way of presenting the superiority of our method, making it accessible to practitioners and researchers in the field. These findings have important implications for improving the accuracy and reliability of solutions to the problem at hand. Overall, our study contributes to the advancement of the field by providing a novel and effective method for solving the problem.