Aspects of the Cycling Phenomenon in the Linear Programming Problem (Lpp) Through the Example of Marshall and Suurballe

A complete analysis of the cycling phenomenon in the case of the linear programming problem (LPP) is far from being achieved. Even if [5] states that the answer to the fundamental question of this problem is found, the proposed solution is very difficult to apply, being necessary to find a solution of a complex system of inequalities. Additionally, it is difficult to recognize a problem that, by applying the primal simplex algorithm, leads us to the occurrence of this phenomenon. The example given by Marshall and Suurballe, but also the example given by Danzig, lead us to draw some useful conclusions about this phenomenon, whether the given problem admits the optimal solution or has an infinite optimal solution