The bullwhip effect is a phenomenon wherein demand fluctuations increase upstream in a supply chain. It can be to reduced through information sharing and demand forecasting. In research on the bullwhip effect for multi-stage supply chain simulations, an approach recommending the use of demand forecast models has been proposed. Since forecast models used in previous studies have been batch learning, they are useful only in situations where sufficient data has already been accumulated. Therefore, it is difficult to apply the batch learning model to a supply chain for which adequate past transaction data is unavailable. In this study, we apply an online learning model to the demand forecaster for a multi-stage supply chain simulation model. We have adopted adaptive regularization of the weight vector as the estimation algorithm for the demand forecaster. Since the proposed model is more powerful than a general online learning algorithm, from the point of view of generalization performance and convergence speed, the proposed method is promising in supply chain simulations. The effectiveness of our approach is confirmed, through computer experiments using the multi-stage supply chain model.