An overview on the simplex algorithm

Algebraic simplex initialization combined with the nonfeasible basis method

“…When the two types of constraints are predominant, the cost generated by adding artificial variables can be prohibitive in number of iterations and therefore in computation time. The nonfeasible basis method, introduced by H. Nabli [10] in 2009 and denoted by NFB, generates an initial feasible basis from an infeasible one, without involving any artificial variables and with no perturbation in the objective function. The idea of this method is to start solving a linear problem by a basis either feasible or infeasible.…”

“…By analogy with the notion of duality in linear programming, the formal tableau satisfies the following property [10]:…”

“…The notion of formal tableau was introduced by H. Nabli [9,10]. For each simplex tableau, a new tableau qualified by formal is constructed.…”

“…This method is a new approach which is completely different from the standard simplex method and also from the dual-simplex algorithm. In the same paper [10], H. Nabli introduced the notion of formal tableau. As a consequence, he developed another new method called formal nonfeasible basis and denoted by FNFB.…”

“…At this stage, the standard simplex algorithm can be executed normally. Recently, H. Nabli [10] suggested a method, termed nonfeasible method (NFB), in order to construct an initial feasible solution from an infeasible one. This method operates without artificial variables or a big M number and without any perturbation in the objective function.…”