Scheduling flexible maintenance activities subject to job-dependent machine deterioration

This paper focuses on single machine scheduling subject to machine deterioration. The current maintenance state of the machine is determined by a maintenance level. While jobs are processed this maintenance level drops by a certain, possibly job-dependent, amount. A maintenance level of less than zero is associated with the machine’s breakdown and is therefore forbidden. Consequently, schedule maintenance activities that raise the maintenance level again may become necessary and have to be scheduled additionally. In what follows, two general types of maintenance activities are distinguished. In the full maintenance case, maintenance activities are always executed until the machine has reached the maximum maintenance level. In contrast to this, the partial maintenance case allows maintenance activities of individual duration. By combining both cases with regular objective functions such as minimization of maximum tardiness, minimization of the sum of completion times, or minimization of the number of tardy jobs, we obtain a new family of specific single-stage scheduling problems. Besides motivating and introducing these problems, the present paper analyzes the computational complexity of general and specific cases.