It is shown that the two machine preemptive job-shop problem with mean flow-time or makespan objective function and three jobs is NP-hard. This contrasts the fact that the nonpreemptive versions of these problems are polynomially solvable if the number of jobs is arbitrary but fixed. It is also...

It is shown that the two machine preemptive job-shop problem with mean flow-time or makespan objective function and three jobs is NP-hard. This contrasts the fact that the nonpreemptive versions of these problems are polynomially solvable if the number of jobs is arbitrary but fixed. It is also...

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...