This study is concerned with the study of the constant due-date assignment policy in a dynamic job shop. Assuming that production times are randomly distributed, each job has a penalty cost that is some non-linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time the job arrives to the shop. This constant time allowed in the shop is the lead time that a customer might expect between time of placing the order and time of delivery. The objective is to minimize the expected aggregate cost per job subject to restrictive assumptions on the priority discipline and the penalty functions. This aggregate cost includes 1) a cost that increases with increasing lead times, 2) a cost for jobs that are delivered after the due dates; the cost is proportional to tardiness and 3) a cost proportional to earliness for jobs that are completed prior to the due dates. The authors present an algorithm for solving this problem and show that the optimal lead time is a unique minimum point of strictly convex functions.