Single machine scheduling jobs with a truncated sum-of-processing-times-based learning effect

In this note, we consider a single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations. We show that even with the introduction of the proposed model to job processing times, several single-machine problems remain polynomially solvable. For the following objective functions, the discounted total weighted completion time, the maximum lateness, we present heuristics according to the corresponding problems without learning effect. We also analyze the worst-case bound of our heuristics.