Minimizing the number of machines for scheduling jobs with equal processing times

In this paper, we consider a parallel machine environment when all jobs have the same processing time and arbitrary release dates and deadlines of the jobs are given. We suppose that the available number of machines, which can be used simultaneously, may vary over time. The aim is to construct a feasible schedule in such a way that the maximal number of simultaneously used machines is minimal. We give a polynomial algorithm for this problem.Parallel machine scheduling Linear programming