Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs

We study a batch delivery single machine scheduling problem where the due dates are controllable and the objective is to minimize earliness, tardiness, holding, due date assignment and delivery costs. The earliness, tardiness and holding cost are assumed to be proportional to the corresponding duration. For each customer order (job) there is a specific acceptable lead time that the customer who placed the order considers to be reasonable and acceptable and therefore there is no penalty by assigning a due date not greater than the acceptable lead time. If the due date is greater than the acceptable date then the due date cost is proportional to the deviation from the acceptable lead time. The batch delivery cost is fixed and there is no capacity limitation on the size of a batch. We provide some properties of the optimal schedule, and prove that the problem is NP-hard. A polynomial time optimization algorithm is presented for two special cases. The first is the case of equal processing times and the second is the case where the acceptable lead times are all equal to zero and the holding penalty is less than the tardiness or due date assignment penalty.