This paper considers the problem of scheduling a set of simultaneously available jobs on several identical machines, and assigning to all jobs a common due-date by which some jobs are early, some are tardy. The objective is to minimize a penalty incurred by the earliness and the tardiness except “just in time”. This paper presents a simple proof of the well known optimality result for the single machine problem that the optimal due-date coincides with one of the job completion times, and shows that the same optimal due-date results can be generalized to the parallel-machine problem. However, the determination of the optimal job sequence for the parallel-machine problem is much more complex. This paper presents a simple heuristic to find an approximate solution.