*Article* **The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect**

**Jin Qian and Yu Zhan \***

College of Science, Northeastern University, Shenyang 110819, China; qianjin@mail.neu.edu.cn **\*** Correspondence: zhanyu@mail.neu.edu.cn

**Abstract:** This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence.

**Keywords:** scheduling; delivery times; learning effect; common due date; slack due date; different due date
