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.