Some results on neighbor robustness of an optimal schedule

The robustness of a schedule is an important problem in practice. In this paper it is studied in the angle that the optimal schedules do not change. Firstly, the neighbor robustness of an optimal schedule is defined, that is the property that an optimal schedule keeps the same when some of the parameters (considered as a point in the responding hyperspace) in the scheduling problem vary in one of its neighbors. Then the results in this paper are proved. The results are: for a problem with continuous objective its strictly optimal schedule is of neighbor robustness, and for single machine total weighted completion time problem its optimal schedule is of neighbor robustness with probability of 1. Some discussion and examples are given.