Single machine rescheduling for new orders with maximum and total time disruption constraints

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 influence the shape of an optimal schedule in particular with respect to the sequencing of old jobs and the insertion of idle time. In this paper, a classification into idle and no-idle problems is given, through several examples, for a set of single machine rescheduling problems with different objective functions. We also prove the complexity of four rescheduling problems that have been left open in the literature. Finally, algorithms are provided to solve the timing problem that arises for certain single machine rescheduling problems when the order of the jobs is fixed.