A note on single-machine scheduling with sum-of-processing-time-based learning and forgetting effects

In this note, we investigate some single-machine problems with both the learning and forgetting effects. A model based on sum-of-processing-time-based learning and forgetting effects are proposed, including some existing models as special cases of our model. Under the proposed model, we derive the optimal solutions for some single-machine problems. Several helpful lemmas are provided to prove various objective functions: the makespan, the total completion time, the total weighted completion time, the total tardiness, and the maximum lateness.