On the modifications of simplex method

Abstract

Simplex Method is one of the most popular methods to solve Linear Programming problems. Many rules and modifications on Simplex Method are proposed to improve the efficiency of iteration. In this study, traditional rules and latest modifications are presented and introduced, focusing either on revision on pivot rules or on method combination. These rules and modifications can surely either reduce the number of pivot steps or simplify calculation. Some of the traditional rules are further modified and even combined so that latest modifications enjoy higher efficiency. For certain methods, further rules are needed to determine the extent to which the method can improve the efficiency.

A Paradigm Shift in Linear Programming: An Algorithm without Artificial Variables

“…This approach markedly reduces the computational time typically consumed by numerous repeated search sequences after each iteration. For further exploration, refer to [12][13][14][15][16][17][18][19][20][21][22]. Notably, the structural underpinnings of most of these methods are rooted in negative variables.…”