A simple proof technique for scheduling models with learning effects

The majority of the previous works concerning scheduling problems with learning effects employed several complicated lemmas to prove the polynomial solvable properties of their models. To simplify these proofs, this paper proposes a simpler technique based on the famous Lagrange mean value theorem and the common adding-and-subtracting-terms operation in mathematics. The re-argumentation of known properties for a general model and the exploitation of a new property verify the effectiveness of this proposed technique and exhibit its simplicity. Moreover, the proof technique is applicable to other similar problems because the technique requires only the prerequisites of the Lagrange mean value theorem.