(601) Operations Research IV Parametric Programming بحوث العمليات البرمجة البارامترية - Taha, Hamdy A. (INP, 2024)
The optimality of the Simplex Method involves two main aspects. First, it must be shown that the iterations will eventually come to an end, meaning that all Zj−jZj−j will reach zero if a finite optimal solution exists. Second, it must be demonstrated that condition 200 implies optimality. The Simplex Method progresses from one basic solution to another, with the new solution often being better than the previous one, and never worse. Therefore, it is generally impossible to return to a previous basic solution. The total number of basic solutions is finite, ensuring the termination of iterations.