Integer preemptive scheduling on parallel machines

We consider preemptive machine scheduling problems on identical parallel machines. It is shown that every such problem with chain-like precedence constraints, release dates and a regular unit-concave objective function (e.g. total weighted tardiness and total weighted number of late jobs) has the following integer preemption property: for any problem instance with integral input data there exists an optimal schedule where all interruptions (as well as starting and completion times of jobs) occur at integer time points.