An on-line scheduling problem of parallel machines with common maintenance time

In this paper, the authors consider an on-line scheduling problem of m (m a parts per thousand yen 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio . In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is .