Some single-machine scheduling problems with past-sequence-dependent setup times and a general learning effect

This paper considers a single-machine scheduling model with past-sequence-dependent setup times and a general learning effect. It develops a general model with setup times and learning effect considerations where the actual processing time of a job is not only a function of the total actual processing time of the jobs already processed, but also a function of the job's scheduled position. The paper shows that the single-machine scheduling problems to minimize the makespan and the sum of the kth power of completion times are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time and the maximum lateness are polynomially solvable under certain conditions.