Single-Machine Scheduling with Aging Effects and Optional Maintenance Activity Considerations

This paper explores a single-machine scheduling with aging effects and the problem regarding optional maintenance activity assignment. The jobs’ processing time is assumed to follow a power position-dependent aging model. The optional maintenance activity refers to the situation in which the maintenance activity can be scheduled immediately after processing of any job has been completed except for the last job and the duration of maintenance activity can be of any value from zero to a fixed time interval. A recovery function is proposed to reflect the efficiency of the machine or worker which is improved. The objective of this study is to decide whether and when to implement the maintenance activity into the job sequence, how long the duration of maintenance activity is, and how to schedule so as to minimize the makespan. Once the duration of maintenance activity is known, we introduce an efficient solution for this problem. In addition, when the maintenance activity is completely performed, we showed that the optimal policy is to schedule the maintenance activity in the middle of the task sequence and optimally solved it by lower order algorithm. Finally, we extend the problem to the case of multiple maintenance activities which are completely performed. Hence, the problem is regarded as polynomial time solvable.