Scheduling on uniform processors with at most one downtime on each machine

We consider the problem of scheduling a given set of tasks on uniform processors with predefined periods of unavailability, with the aim of minimizing the maximum completion time.We give a simple polynomial MULTIFIT-based algorithm, the schedules of which finish within 1.5 times the maximum between the latest end of a downtime and the end of the optimal schedule, when there is at most one downtime on each machine. Even when all processors have the same processing speed, it is NP-hard to obtain schedules that obey better bounds for this problem.