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 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. This class of objective functions includes such classical objective functions as total weighted tardiness and total weighted number of late jobs.