一类Flow Shop调度问题最优调度区间摄动鲁棒性

Interval perturbation robustness of optimal schedules for a class of Flow Shop problems

调度的鲁棒性是调度应用中的一个重要问题.本文从最优调度不变的角度研究了调度的鲁棒性问题.首先定义了最优调度的区间摄动鲁棒性,即当问题中某些参数在各自的区间上变化时最优调度保持不变的性质.然后对比例FlowShop调度问题(任给一个工件它在各台机器上的加工时间都相同)进行了研究.通过一个引理我们证明了本文的结果,该引理指出了r个参数的大小次序与它们的变化区间的相交关系之间的联系.本文的结果是目标函数为完成时间总和时在加工时间扰动下最优调度具有区间摄动鲁棒性的三个充分必要条件,目标函数为最大拖期时间时及目标函数为拖后工件个数时在加工时间和/或交付期扰动下最优调度具有区间摄动鲁棒性的若干充分条件.这些结果与调度在一个由变化参数构成的超矩形的一些顶点上的最优性有关.文中给出了使用这些结果的例子.

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.