Single machine scheduling with multiple common due date assignment and aging effect under a deteriorating maintenance activity consideration

In this paper, we consider the multiple common due date assignment and single machine scheduling with a job-dependent aging effect and a deteriorating maintenance activity. Once the maintenance activity has been completed, the machine will revert to its initial condition and the aging effect will start anew, the maintenance duration depends on its starting time. The objective is to minimize the total of earliness, tardiness, due date costs and find the optimal due date, the optimal maintenance position. We introduce an efficient O(n ⁴) algorithm to solve the problem. We also provide a special case of the problem and show that it remains polynomial time solvable.