Development of Simplex Method in Linear Programming: A Review of Artificial-Free Simplex Method, Big-M, and its Various Applications in Optimization

Abstract

Linear programming is one of the most widely used optimization methods in managerial decision-making. Among the various algorithms developed to solve linear programming problems, the Simplex Method remains one of the most popular and effective approaches. As optimization needs to continue to evolve, researchers have sought to improve the efficiency and effectiveness of the Simplex Method through the development of new algorithms and its application across various sectors. This article aims to review the development of the Simplex Method based on five scientific articles covering the Artificial-Free Simplex Method (ASM), modifications of the Big-M Method, the application of the Simplex Method in communication module production, various industrial applications of the Simplex Method, and the development of the Infinite Big-M Method. The study employs a literature review approach using a qualitative descriptive method. The review findings indicate that the Simplex Method remains a relevant optimization tool in various fields due to its ability to regularly generate optimal solutions. Furthermore, several developments and modifications have successfully addressed some limitations of the conventional Simplex Method, particularly those related to the use of artificial variables, the determination of penalty parameter M values, and computational efficiency. Therefore, this study highlights the significant role of the Simplex Method in supporting data-driven decision-making, especially in the fields of management and industry.