Single-machine group scheduling with time-dependent learning effect and position-based setup time learning effect

As to learning effect, it may be more appropriate to assume that position-based learning takes place during machine setups only, while sum-of-processing-time-based learning occurs in considering the experience that workers have gained from producing jobs. Thus, in this paper, we consider sum-of-processing-time-based learning on job processing time and position-based learning on setup time in single-machine group scheduling problems. The objectives are to minimize the makespan and the total completion time, respectively. We provide two polynomial time algorithms to solve the makespan minimization problems. On the other hand, we also provide two polynomial time algorithms to solve the total completion time minimization problems under certain conditions.