Parallel-machine scheduling with linear deteriorating jobs and preventive maintenance activities under a potential machine disruption

This paper studies linear deteriorating jobs and maintenance activities under the potential disrupted parallel machines. Potential disruption means that there exists an unavailable interval at a particular time under a certain probability on some machine. We consider the resumable case and the non-resumable case when a machine becomes available again. Under the disturbed machine, a potential maintenance service is performed, which a maintenance activity will return to its original state efficiency. The objective function is to minimize the expected sum of completion times for the non-resumable case and the resumable case. By dividing maintenance interval into before the disturbance interval, the overlapping part of the maintenance interval and the disturbance interval, and after the disturbance interval, we determine time complexity analysis of various cases, and present the pseudo-polynomial time algorithms for them, respectively.