A revision of machine scheduling problems with a general learning effect

In this paper, we show that the main results in a recent paper by Zhang and Yan [X. Zhang and G. Yan, Machine scheduling problems with a general learning effect, Mathematical and Computer Modelling 51 (2010) 84-90] are incorrect as an important reason is missing, that is, the processing time of a job is variable according to a general learning effect. Here we point out these wrong results by a counter-example. In addition, we give a revised model with a general learning effect. We show that some single machine scheduling problems are still polynomially solvable under the revised model. We also show that some special cases of the flowshop scheduling problems can be solved in polynomial time under the revised model.