Interval perturbation robustness of optimal schedules for a class of Flow Shop problems
一类 Flow Shop 调度问题最优调度区间摄动鲁棒性

The robustness of schedules is an important problem in practice. It was studied in the angle that the optimal schedules do not change. Firstly the interval perturbation robustness of an optimal schedule was defined, that was 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 proportionate flow shop, where the processing time of any given job on every machine is the same, was 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 were proved. The results are three necessary and sufficient conditions for the objective of total completion time and some sufficient conditions for the objective of maximum lateness time or for the objective of the number of tardy jobs 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 consisting of the varying parameters. Some examples that showed how to use these results were given.