Rescheduling to trade off between global disruption of original jobs with flexibility and scheduling cost of new jobs

In this paper we introduce and study the rescheduling problem to trade off between global disruption of the original jobs with flexibility and the scheduling cost of the new jobs. A set of original jobs has been scheduled on a single machine. But before the processing of original jobs begins, a set of new jobs arrives unexpectedly. The scheduler needs to adjust the existing schedule with a view to finding a cost-efficient schedule for the new jobs without causing too much disruption of the original schedule. We make three assumptions that are different from those in the literature: (i) the original jobs are regarded as a unified whole (a big job) and the global disruption of the original jobs is considered, (ii) the original jobs can be split into small pieces in a schedule, which enables effective control of the global disruption, and (iii) the cost of the original jobs depends on the global disruption, while the cost of the new jobs is expressed as a regular scheduling criterion, such as the maximum lateness, the total weighted completion time, and total weighted number of tardy jobs. We analyze the computational complexity of variants of the rescheduling problem.