Single-machine scheduling problems with the time-dependent learning effect

In this paper, three single-machine scheduling problems with time-dependent learning effect model to minimize the sum of weighted completion times, the sum of the kkth powers of completion times and the maximum lateness are investigated. We show that the shortest processing time first (SPT) rule is an optimal solution for the problem to minimize the sum of the kkth powers of completion times. Some polynomial time solutions are provided for the other two problems under certain conditions, respectively.