Lot-Order Assignment Applying Priority Rules for the Single-Machine Total Tardiness Scheduling with Nonnegative Time-Dependent Processing Times

Lot-order assignment is to assign items in lots being processed to orders to fulfill the orders. It is usually performed periodically for meeting the due dates of orders especially in a manufacturing industry with a long production cycle time such as the semiconductor manufacturing industry. In this paper, we consider the lot-order assignment problem (LOAP) with the objective of minimizing the total tardiness of the orders with distinct due dates. We show that we can solve the LOAP optimally by finding an optimal sequence for the single-machine total tardiness scheduling problem with nonnegative time-dependent processing times (SMTTSP-NNTDPT). Also, we address how the priority rules for the SMTTSP can be modified to those for the SMTTSP-NNTDPT to solve the LOAP. In computational experiments, we discuss the performances of the suggested priority rules and show the result of the proposed approach outperforms that of the commercial optimization software package.