Artificial-Variable-Free simplex method for frimal and dual linear programming models

Abstract

Solving a general linear programming problem using the simplex algorithm relies on introducing artificial variables that deals with a large search space. This dissertation presents the non-acute constraint relaxation technique that not only eliminates the need for artificial variables but also reduces the start-up time to solve the initial relaxation problem. To guarantee the optimal solution or infeasibility or unboundedness of a linear programming problem, the algorithm reinserts the non-acute constraints back to the relaxation problem. The results of this algorithm are superior than the original simplex algorithm with artificial variables for a linear programming problem which the relaxed problem obtains the optimal solution before the the reinsertion of non-acute constraints.