Single-machine scheduling with an actual time-dependent learning effect

In this study, we introduce an actual time-dependent learning effect into single-machine scheduling problems. The actual time-dependent learning effect of a job is assumed to be a function of the total actual processing time of jobs scheduled in front of it. We introduce it into single-machine scheduling problems and we show that it remains polynomially solvable for three objectives, that is, minimizing the makespan, the total completion time and the sum of the kth power of completion times. We also provide a polynomial time solution to minimize the sum of the weighted completion times if jobs have agreeable weights.