Parallel machine makespan minimization subject to machine availability and total completion time constraints

In this paper, we study the parallel machine scheduling subject to machine availability constraint. The jobs can be resumed after being preempted by another job or interrupted by the unavailable intervals. The goal is to minimize the makespan subject to the constraint that the total completion time is minimized. We study two different machine unavailability models. In the first model, each machine has a single unavailable interval which starts from time 0. In the second model, each machine can have multiple unavailable intervals, but at any time, there is at most one machine unavailable. For each model, we show that there is an optimal polynomial time algorithm.