Minimizing number of tardy jobs on a single machine subject to periodic maintenance

This paper considers a single-machine scheduling problem with periodic maintenance. In this study, a schedule consists of several maintenance periods and each maintenance period is scheduled after a periodic time interval. The objective is to find a schedule that minimizes the number of tardy jobs subject to periodic maintenance and nonresumable jobs. Based on the Moore's algorithm, an effective heuristic is developed to provide a near-optimal schedule for the problem. A branch-and-bound algorithm is also proposed to find the optimal schedule. Some important theorems associated with the problem are implemented in the algorithm. Computational results are presented to demonstrate the effectiveness of the proposed heuristic.