The interval perturbation robustness of an optimal schedule for single machine discounted total weighted completion time problem

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 interval perturbation robustness of an optimal schedule is defined, that is the property that an optimal schedule keeps the same when some of the parameters in the scheduling problem vary in some intervals. Then the interval perturbation robustness of an optimal schedule for single machine discounted total weighted completion time is studied. Form a lemma that gives the relationship between the order of r parameters and the overlaps between each two of the intervals in which these parameters vary, the results in this paper are proved. The results are three if and only if conditions under which an optimal schedule is of interval perturbation robustness. These results relate to the optimality of a schedule at some of the vertices of a hyperrectangle of r dimension consisting of the varying parameters. Some examples that show how to use these results are given.