Maximizing the weighted number of just-in-time jobs in flow shop scheduling

In this paper we consider the maximization of the weighted number of just-in-time jobs that should be completed exactly on their due dates in n-job, m-machine flow shop problems. We show that a two-machine flow shop problem is NP-complete. When job weights are all identical, we show that the problem can be solved in polynomial time. We also show that a three-machine flow shop problem with identical job weights is NP-hard in the strong sense by reduction of the 3-partition problem.