This article reviews the main progress in studying the bullwhip effect in supply chains and the argument about the validity of the production2smoothing model . Some of our very recent achievements in these two areas are also introduced. Our work integrates a general ARIMA (autoregressive integrated moving average) demand process into a multi2stage supply chain , and by the integrated model studies systematically the propagation rules of the de2 mand information flow. The findings of these propagation rules revoke some classical conclusions on the bullwhip ef2 fect , reveal some important and novel phenomena and provide a reasonable explain on the validity of the production2 smoothing model . Three questions are also asked for further investigations in the field.