A scheduling model with a more general function of learning effects

•The proposed model is more general.•Both the normal processing case and the actual processing case are considered.•The proof technique is simpler and easier to use.

This study develops a more general model for scheduling problems with learning effects. Compared with the existent general models, the proposed time- and position-dependent model simultaneously covers the normal and actual processing cases. Moreover, the model has many new properties that the previous work did not study. In this paper, a distinctive proof technique is developed based on the adding-and-subtracting-terms operation and the Lagrange Mean Value Theorem. The proof technique is easier to use than the method based on multiple identical or similar lemmas employed in a large number of literatures.