Optimal due date assignment in multi-machine scheduling environments

We study two due date assignment problems in various multi-machine scheduling environments. We assume that each job can be assigned an arbitrary non-negative due date, but longer due dates have higher cost. The first problem is to minimize a cost function, which includes earliness, tardiness and due date assignment costs. In the second problem, we minimize an objective function which includes the number of tardy jobs and due date assignment costs. We settle the complexity of many of these problems by either showing that they are NP -hard or by providing a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.