Scheduling flexible maintenance activities subject to job-dependent machine deterioration

Abstract

This paper considers single machine scheduling that integrates machine deterioration. The current maintenance state of the machine is determined by a maintenance level which drops by a certain, possibly job-dependent, amount while jobs are processed. A maintenance level of less than zero is associated with the machine's breakdown and is therefore forbidden. Consequently, 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 schedule in the partial maintenance case has to additionally determine the duration of maintenance activities. 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 set of specific single-stage scheduling problems. Besides motivating and introducing these problems, we shall also analyze the computational complexity of general and specific cases.