 Greatest improvement pivot rule

For a feasible simplex dictionary, let $r_j>0$ be a nonbasic variable's improving reduced cost and let ${\theta }_j$ be its largest feasible increase from the simplex ratio test. The greatest improvement pivot rule chooses an entering variable maximizing $r_j{\theta }_j$. It measures the improvement over the entire edge, whereas the Dantzig pivot rule maximizes only $r_j$.

// Target: mathematical-optimization.bigb