Single-machine and flowshop scheduling with a general learning effect model

Learning effects in scheduling problems have received growing attention recently. Biskup [Biskup, D. (2008). A state-of-the-art review on scheduling with learning effect. European Journal of Operational Research, 188, 315–329] classified the learning effect scheduling models into two diverse approaches. The position-based learning 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 model takes into account the experience the workers gain from producing the jobs. In this paper, we propose a learning model which considers both the machine and human learning effects simultaneously. We first show that the position-based learning and the sum-of-processing-time-based learning models in the literature are special cases of the proposed model. Moreover, we present the solution procedures for some single-machine and some flowshop problems.