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.

This paper considers the single-group scheduling models with Pegels’ and DeJong’s learning effect and the single-group scheduling models with Pegels’ and DeJong’s aging effect. In a classical scheduling model, Pegels’ and DeJong’s learning effect is a constant or position-dependent, while the learning effect and aging effect are job-dependent in this paper. Compared with the classical learning model and aging model for scheduling, the proposed models are more general and realistic. The objective functions are to minimize the total completion time and makespan. We propose polynomial time methods to solve all the studied problems.