TITLE:
Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches
AUTHORS:
Abdur Rashid, Md. Amirul Islam
KEYWORDS:
Transportation Problem, Initial Basic Feasible Solution, Optimal Solution, Two Reliable Approaches (theorems) and Numerical Illustrations
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.4,
December
13,
2023
ABSTRACT: In this paper, we have used two reliable approaches (theorems) to find
the optimal solutions to transportation
problems, using variations in costs. In real-life scenarios,
transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation
problem in the context of variations
in cost is vital for ensuring cost efficiency, resource allocation,
customer satisfaction, competitive advantage, environmental responsibility,
risk mitigation, and operational fortitude in practical situations. This paper
opens up new directions for the solution of transportation problems by
introducing two key theorems. By using these theorems, we can develop an
algorithm for identifying the optimal solution attributes and permitting
accurate quantification of changes in overall transportation costs through the
addition or subtraction of constants to specific rows or columns, as well as
multiplication by constants inside the cost matrix. It is anticipated that the
two reliable techniques presented in this study will provide theoretical
insights and practical solutions to enhance
the efficiency and cost-effectiveness of transportation systems.
Finally, numerical illustrations are presented to verify the proposed
approaches.