Scheduling jobs in open shops with limited machine availability

In this paper, open shop scheduling problems with limited machine availability are studied. Such a limited availability of machines may appear in many real-life situations, e.g. as preventive maintenance activities. Three types of jobs are distinguished: nonpreemptable, resumable and preemptable. An operation of a resumable job if not completed before a non-availability period of a machine may be suspended and continued without additional cost when the machine becomes available. In the paper, results are given for the scheduling problems associated with the three types of jobs. For preemptable jobs polynomial-time algorithms based on the two-phase method are proposed.