Prediction of demand plays a critical role in replenishment, in supply chain management. Accurate prediction of demand is a fundamental requirement and is also a great challenge to demand prediction models. This has motivated the research team to develop the minimum description length (MDL)-optimal neural network (NN) which can accurately predict retailer demands with various time lags. Moreover, a surrogate data method is proposed prior to the prediction to investigate the dynamical property (i.e., predictability) of various demand time series so as to avoid predicting random demands. In this paper, we validate the proposed ideas by a full factorial study combining its own decision rules. We describe improvements to prediction accuracy and propose a replenishment policy for a Hong Kong food wholesaler. This leads to a significant reduction in its operation costs and to an improvement in the level of retailer satisfaction.