Revised Delivery-Time Quotation in Scheduling with Tardiness Penalties

There are many situations in supply chain scheduling when the supplier finds it impossible to meet the promised due dates for some orders. We present a model for the rescheduling of orders with simultaneous assignment of attainable revised due dates to minimize due date escalation and tardiness penalties for the supplier. We show that the problem is equivalent to minimizing the total tardiness with rejection with respect to the original due dates. We prove that the problem is NP-hard and present a pseudopolynomial algorithm for it. We also present a fully polynomial time approximation scheme for the problem. Finally, we discuss the implications of our solution for setting fair tardiness penalties when due dates have to be renegotiated because of the delays.