Financial analyses of on-line preemption-restart scheduling subject to cost penalties

This paper considers the on-line production order scheduling problem where each preemption causes a penalty, and the net profit is the total revenues of completed jobs minus the total penalties caused by preemptions. We discuss a preemptive version of the single-machine scheduling problem with the total flow time criterion. Two models with different kinds of preemption cost penalties are considered in this paper. In the first model, cost penalties are constant. In the second model, the preemption penalties are proportional to the lost part of the preempted job. Uncertain release times and processing times are modeled by an M/M/1 queue system. We calculate a lower bound probability for preemption of each job. Also, some financial analyses of the models are presented.