On scheduling problems with the aging effect and maintenance cost

In this paper, we analyse the single machine scheduling problem with the aging effect and maintenance activities in which the actual processing time is a non-decreasing function dependent on a condition of a machine. With the performed jobs the condition of the machine decreases and the time necessary to process a job increases. To improve the condition of a machine maintenance activities can be performed, however there is a cost related to each maintenance activity. The objectives considered are the minimisation of the makespan under a given total maintenance cost as well as the minimisation of the total maintenance cost under given makespan criterion. The computational complexity of the problems is determined and solution properties are proved.