Scheduling Deteriorating Jobs with a Common Due Window on a Single Machine

We consider the problem of scheduling deteriorating jobs and common due window location on a single machine. The actual processing time of a job is a linear increasing function of its starting time. The problem is to determine the optimal earliest due date, the due window size and the job schedule simultaneously to minimize costs for earliness, tardiness, earliest due date assignment and due window size penalties. A polynomial time optimal algorithm is presented to solve the problem.