Rescheduling problems arise in a variety of situations where a previously planned schedule needs to be adjusted to deal with unforeseen events. A common problem is the arrival of new orders, i.e. jobs, which have to be integrated into the schedule of the so-called old jobs. The maximum and total absolute time deviations of the completion times of these jobs are modeled as a disruption constraint to limit the change in the original schedule. Disruption constraints affect the shape of an optimal schedule, particularly with respect to the sequencing of old jobs and the insertion of idle time. We therefore give a classification into idle and no-idle problems for a set of single-machine rescheduling problems with different objective functions. We then prove the complexity of five rescheduling problems that have been left open in the literature.

翻译：重调度问题出现在多种需要调整原计划以应对突发事件的场景中。一个常见问题是新订单（即作业）的到达，这些新订单必须整合到所谓旧作业的调度中。旧作业完工时间的最大绝对时间偏差与总绝对时间偏差被建模为一种中断约束，以限制原调度的变化。中断约束会影响最优调度的形态，特别是在旧作业的排序以及空闲时间的插入方面。为此，我们对一组具有不同目标函数的单机重调度问题进行了空闲问题与无空闲问题的分类。随后，我们证明了文献中遗留的五个重调度问题的复杂性。