Predicting the amount of sales in the future is a fundamental problem in the replenishment process of retail companies. Models for forecasting the future demand of an item typically rely on influential features and historical sales of the item. However, the values of some influential features (to which we refer as non-plannable features) are only known during model training (for the past), and not for the future at prediction time. Existing forecasting methods ignore such non-plannable features or wrongly assume that they are also known at prediction time. We identify non-plannable features as privileged information, i.e., information that is available at training time but not at prediction time, and propose a neural network architecture to leverage this source of data accordingly. We present a dual branch neural network architecture that incorporates non-plannable features at training time, with a first branch to embed the historical information, and a second branch, the PI branch, to predict demand based on privileged information. Next, we leverage a single branch network at prediction time, which applies a simulation component to mimic the behavior of the PI branch, whose inputs are not available at prediction time. We evaluate our approach on two real-world forecasting datasets, and find that it outperforms state-of-the-art competitors in terms of mean absolute error and symmetric mean absolute percentage error metrics. We further provide visualizations and conduct experiments to validate the contribution of different components in our proposed architecture.