Scheduling maintenance activities subject to stochastic job-dependent machine deterioration

This paper considers a maintenance scheduling problem on a single machine with a fixed job sequence involving job-dependent, stochastic deterioration. If the machine breaks down, then a time-consuming emergency maintenance activity needs to be conducted. Instead, planned maintenance activities can be conducted between jobs in order to improve the machine’s state and, thus, prevent the machine from breaking down. We distinguish two types of machines differing in the flexibility regarding the point of time when the maintenance activities need to be scheduled. The goal is to minimize the total expected completion time of jobs. We formalize two optimization problems, analyze their computational complexities, develop exact solution approaches, and conduct a computational study. Here, we show that our approaches can solve large instances to optimality within short run times and we analyze the advantage gained by planning maintenance activities depending on the actual state of the machine.