Single-machine scheduling with a time-dependent learning effect

In this paper we consider the single-machine scheduling problem with a time-dependent learning effect. The time-dependent learning effect of a job is assumed to be a function of the total normal processing time of the jobs scheduled in front of the job. We show by examples that the optimal schedule for the classical version of the problem is not optimal in the presence of a time-dependent learning effect for the following three objective functions: the weighted sum of completion times, the maximum lateness and the number of tardy jobs. But for some special cases, we prove that the weighted shortest processing time (WSPT) rule, the earliest due date (EDD) rule and Moore's Algorithm can construct an optimal schedule for the problem to minimize these objective functions, respectively.