On single processor scheduling problems with learning dependent on the number of processed jobs

The importance of the role that learning plays in manufacturing, industry and computer systems is undeniable as well as the profit that can be increased if this phenomenon is taken into consideration for short- and long-term optimization. In this paper, we focus on scheduling jobs on a single processor, where its effectiveness can increase with the number of processed jobs, to minimize one of the following objectives: the maximum completion time with the release dates, the maximum lateness and the number of late jobs. It is proved that these well known polynomially solvable problems become at least NP-hard with the considered learning models. To solve them we provide some elimination procedures that are used to construct a branch and bound algorithm. Furthermore, we propose some fast heuristics for the problem of minimizing the number of late jobs with the general model of the learning effect.