Amaliah, B., Fatichah, C. and Suryani, E. (2019) Total Opportunity Cost Matrix-Minimal Total: A New Approach to Determine Initial Basic Feasible Solution of a Transportation Problem. Egyptian Informatics Journal, 20, 131-141.
https://doi.org/10.1016/j.eij.2019.01.002

has been cited by the following article:

• 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.