A note on flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

The main results in a recent paper [M. Cheng, S. Sun, L. He, Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines, European Journal of Operational Research 183 (2007) 115-124] are incorrect because job processing times are variable due to deteriorating effect, which is not taken into account by the authors. In this note, we show first by counter-examples that the published results are incorrect, and then we provide corrected results.