Idle Time Treatment in the Single-Machine Scheduling Problem With Distinct Release Dates

The purpose of this study is to examine how idle time treatment in the single-machine scheduling problem with distinct (unequal) release dates affects schedules. For this purpose, two types of settings are considered: any idle time is permitted and unforced idle time is forbidden. In the latter setting, idle time is permitted only when no jobs are available, that is, release dates of unprocessed jobs are larger than the current time instant. Under these two idle time settings, the problem is solved both offline and online. In offline scheduling, all job information is known in advance and the schedule is optimized only once at time zero while in online scheduling, the schedule is re-optimized for only currently available jobs every time when a new job becomes available at its release date. Benchmark instances in the literature are solved by these approaches and the effect of idle time treatment on the obtained schedules is examined.