Single machine scheduling with fuzzy preemption penalties

In preemptive scheduling problems, processing of a job can be temporarily interrupted, and resumed at a later time. Conventionally, in the literature on preemptive scheduling, preempted jobs can simply be resumed from the point at which preemption occurred or restart from the beginning. However, this situation may not always be true in practice. It is likely that, in some cases, an imprecise or fuzzy part of jobs processing must be repeated, i.e., a fuzzy time penalty must be incurred. In this paper, we consider the single-machine scheduling problem of minimizing the total flow time subject to job release dates and fuzzy preemption penalties. We present a heuristic algorithm and validate it using some numerical examples.