The Single-Machine Preemptive or Resumable Scheduling with Maintenance Intervals

We study the single-machine scheduling with maintenance intervals under preemptive pattern and resumable pattern, respectively, to minimize the total weighted late work and the weighted number of tardy jobs, respectively, where each job has a release date and a due date. According to the different combinations of the two scheduling patterns and the two scheduling criteria, six scheduling problems (including two Pareto-scheduling problems) are studied in this paper. We show that by modifying the release dates and the due dates, the six problems can be reduced to their corresponding scheduling problems without maintenance intervals in quasi-linear time. As a consequence, complexity results of our problems can be directly obtained from the known results in the literature. In particular, for the problem under resumable pattern to minimize the total weighted late work with all the jobs being released at time 0, an O(mn(2)P)-time algorithm was presented in the literature, where m is the number of maintenance intervals, n is the number of jobs, and P is the total processing time of the jobs; and our research shows that the same problem is solvable in O(n(2) P + m log m) time, improving this known result.