Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches
- 1 Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
- 2 Department of Mathematics, Uttara University, Dhaka, Bangladesh
Abstract
In this paper, we have used two reliable approaches (theorems) to find the optim al solutions to transportation problems, using variations in costs. I n real-life scenarios, transportation costs can fluctuate due to different factors. Find ing optimal solutions to the transportation problem in the context of varia tions in cost is vital for ensuring cost efficiency, resource allocat ion, 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 an d practical solutions to enhance the efficiency and cost-effectiveness o f transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.
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