Single - machine Scheduling with Position - based and Sum - of - processing - time - based Learning Effects

The learning effects are widely studied in scheduling problems recently. Biskup [1] classified the learning effect models into two diverse approaches, namely the position -based and the sum-of-processing-time-based learning effect models. He further claimed that the position-based learning effect model seems to be a realistic assumption for the case that the actual processing of the job is mainly machine-driven, while the sum-of-processing-time -based learning effect model takes into account the effects that the human gains from the experience of operating similar tasks. In this paper, we propose a learning model which considers both the machine and human learning effects simultaneously. We will show that the position-based learning and the sum-ofprocessing-time-based learning effect models are special cases of the proposed model. Moreover, we will derive the optimal solutions for some single-machine problems.