An Equivalent Condition of Two-Machine System Scheduling with Robustness Under a Class of Linear Perturbation

The equivalent conditions of two-machine system scheduling problem with robustness is studied by using a property of Abelian semi-group which containing identity element on the real set. According to the practical problem, we construct a class of linear perturbation system model, propose the system output expression, and give its some properties. Finally, by the definition of optimal robust scheduling, we prove that the condition of the optimal scheduling robustness criterion of referential system is equivalent to the condition of its optimal scheduling criterion