Preemptive scheduling of jobs with agreeable due dates on a single machine to minimize total tardiness

We consider the problem of scheduling n preemptive jobs on a single machine to minimize total tardiness, subject to agreeable due dates, i.e., a later release date corresponds to a later due date. We prove that the problem is NP-hard in the ordinary sense by showing that it is NP-hard, and deriving a pseudo-polynomial algorithm for it.