A New Method to Determine the Entering Variable in Simplex Algorithm

Simplex method was developed by Dantzig at first about a half century ago as an algorithm for solving linear programming (LP) problems. Currently, one might hardly find a serious scholar who is unaware of LP and/or the simplex method entirely. Although there is interior point methods algorithm (such as karmarkar algorithm) have been developed for solving LP problems in polynomial time, but simplex method is very popular as an algorithm for solving these problems, too. Despite of the popularity of this algorithm, one is considerable that simplex solves some of LP problems in exponentially time, such as Klee-Minty cube and therefore need to be modified to achieve better performance. This paper will introduce a new method for determining the entering variable in which the minimum ratio test is considered in this regard. The experiments affirm the superiority of the novel scheme.