New variants of finite criss-cross pivot algorithms for linear programming

A study was conducted to generalize the first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex technique to the criss-cross pivot setting. The finiteness of the new criss-cross pivot variants was proven. Results indicated that the finiteness of the criss-cross algorithms A1, A2 and A3 work in a recursive manner, always solving a subproblem completely before considering a larger subproblem.