Max-out-in pivot rule with cycling prevention for the simplex method

Abstract

A max-out-in pivot rule is designed to solve a linear programming (LP) problem with a non-zero right- hand side vector. It identifies the maximum of the leaving basic variable before selecting the associated entering nonbasic variable. Our method guarantees convergence after a finite number of iterations. The improvement of our pivot rule over Bland's rule is illustrated by some cycling LP examples. In addition, we report computational results obtained from two sets of LP problems. Among 100 simulated LP problems, the max-out-in pivot rule is significantly better than Bland's rule and Dantzig's rule according to the Wilcoxon signed rank test. Based on these results, we conclude that our method is best suited for degenerate LP problems.