Parallel machines scheduling with machine shutdowns

We study the nonpreemptive parallel machines scheduling problem where some of the machines are planned to be shutdown. We apply longest processing time (LPT) algorithm to the problem and analyze its performance. Our analysis shows that the makespan of the LPT schedule is bounded by twice the optimum makespan if no more than half of the machines are allowed to be shutdown simultaneously. We also show that this bound is tight by constructing a worst-case example.