Several single-machine scheduling problems with general learning effects

In this paper we consider several single-machine scheduling problems with general learning effects. By general learning effects, we mean that the processing time of a job depends not only on its scheduled position, but also on the total normal processing time of the jobs already processed. We show that the scheduling problems of minimization of the makespan, the total completion time and the sum of the θ  th (θ⩾0θ⩾0) power of job completion times can be solved in polynomial time under the proposed models. We also prove that some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time.