In this paper, a generalized model with past-sequence-dependent learning and forgetting effects is proposed. Both effects are assumed to be dependent on the sum of processing time as well as the scheduling position. Based on this model, we investigate and prove that some single-machine problems remain polynomially solvable with certain agreeable conditions. We further show that many models known in the literature are special cases of our proposed model. Several helpful lemmas are presented to analyze single-machine scheduling problems with various objective functions: makespan, total completion time, weighted completion time, and maximum lateness.