A note on a due-date assignment on a two-machine flow-shop

We address a due-date assignment and scheduling problem in a two-machine flow-shop setting. Our objective is to find both the job schedule and the common due-date which minimize maximum earliness, tardiness and due-date costs. We introduce an efficient (O(n² log n)) solution, based on repetitive use of the well-known Johnson Algorithm. Careful determination of the due-date in the course of sales negotiations with a customer is clearly an important task for the firm. A late due-date reflects a lower service level and incurs an obvious penalty for the supplier. For a given due-date, there are penalties associated with jobs completed early or late. This paper addresses a Just-In-Time scheduling problem incorporating all these cost components. The machine setting assumed is a two-machine flow-shop. We show that an optimal solution (i.e., both an optimal due-date value and an optimal job schedule) can be found in polynomial time.