Scheduling maintenance activities subject to continuous stochastic job-dependent machine deterioration

In this paper, we consider a single machine scheduling problem with a fixed job sequence involving job-dependent deterioration and maintenance activities. The deteriorations underlie continuous probability distributions and degrade the machine’s state. Deteriorations may lead to a machine breakdown, which demands a time-consuming maintenance activity. To prevent the machine from breaking down, planned maintenance activities can be scheduled between jobs in order to restore the state of the machine. Thereby, the current state of the machine is observable at the completion of any job and is decisive for the decision about planning a maintenance activity. The goal is to minimize the expected total completion time of the jobs in the sequence. We formalize the optimization problem, formulate a dynamic programming formulation representing the problem, and present different heuristic solution approaches. In a computational study we analyze the results for the different proposed solution approaches and show that multiple approaches provide good solutions for the scheduling of planned maintenance activities.