Automatic small parts warehouses (ASPW) are often used for the picking of small parts in distribution warehouses. Usually, only small amounts of the articles delivered on pallets are repacked into containers and stored into the ASPW, where these articles can be quickly provided for picking. The remaining quantities are taken to a pallet warehouse (replenishment storage). Only when the stock level in the ASPW falls below a predefined value, replenishment is requested. This thesis deals with the optimization of the replenishment control for such an ASPW and in particular with the question whether machine learning methods can be used for that purpose. After a short theoretical introduction to warehousing and picking, the basics for the practical part are introduced. The considered warehouse and the relevant processes are described as well as the way how data was obtained and prepared. Afterwards, the current procedure for replenishment control in the considered ASPW is specified and critically reviewed. It turns out that a basic assumption made about the statistical distribution of the required quantities does not hold. Thus, it is finally attempted to achieve a good demand forecast by using machine learning. In addition, the theoretical basics are explained for each of these steps.