The simplex method

∗Most of the material is from [1] When this assumption is violated, a degenerate basic variable (with zero value) occurs in a basic feasible solution. Often it can be handled as a nondegenerate basic feasible solution. However, it is possible that at pivoting the new variable will come in at zero value. This implies that the zero-valued basic variable is the one to go out. The objective will not decrease and the new basic feasible solution will also be degenerate. The result is a cycle that could be repeated indefinitely. Methods have been developed to avoid such cycles [1, pp. 78].