Single-Machine Scheduling with Due-Date Assignment and Aging Effect under a Deteriorating Maintenance Activity Consideration

This study investigates single-machine due-date assignment and scheduling problems with a job-dependent aging effect under a deteriorating maintenance activity consideration simultaneously. The maintenance activity can be scheduled immediately after any one of the jobs has been completed. In order to model the problem more realistic, we assume that: (1) once the maintenance activity has been completed, the machine will revert to its initial condition and the aging effect will start anew, and (2) the machine maintenance duration depends on its starting time. The objective is to find the optimal maintenance position as well as the optimal location of the common due-date for minimizing the total of earliness, tardiness and due-date costs. We introduce a polynomial O(n) time solution for the problem. We also present two special cases of the problem and show that they can be optimally solved by a lower order algorithm.