Max-out-in pivot rule with Dantzig's safeguarding rule for the simplex method

Abstract

The simplex method is used to solve linear programming problem by improving the current basic feasible solution. It uses a pivot rule to guide the search in the feasible region. The pivot rule is used to select an entering index in simplex method. Nowadays, many pivot rule have been presented, but no pivot rule shows superior performance than other. Therefore, this is still an active research in linear programming. In this research, we present the max-out-in pivot rule with Dantzig's safeguarding for simplex method. This rule is based on maximum improvement of objective value of the current basic feasible point similar to the Dantzig's rule. We can illustrate by Klee and Minty problems that our rule outperforms that of Dantzig's rule by the number of iterations for solving linear programming problems.