Integrated production scheduling and periodic maintenances on a single machine with release dates

This paper addresses the production scheduling problem on a single machine with periodic maintenances, where the jobs´ release dates are considered. For the resumable case, we prove that the problem can be solved in polynomial time. For the non-resumable case, we prove that the problem is strongly NP-Hard and propose an effective heuristic ERD-LPT based on the properties of optimal solutions. Then a branch-and-bound algorithm (B&B) that utilizes several dominance rules is developed to search the optimal schedules for the small-to-medium sized problems. Computational results indicate that the proposed heuristic is highly accurate compared with B&B and the improvement of performance is significant compared with the First-in-First-out (FIFO) rule.