We consider a computer manufacturer who assembles customized final products from various components. Customer orders specify the product configuration, the quantity and a desired delivery date. The online order promising (OP) process must announce a first promised delivery date to the customer. Demand fulfillment in this Assemble-to-Order (ATO) case is still little investigated and differs remarkably from the more popular Make-to-Stock (MTS) case: Bottlenecks are the assembly capacity and the stocks of components, which are available to promise (ATP). An important task of the demand fulfillment, besides OP, is Demand Supply Matching (DSM), i.e. deciding on the assembly date of orders and eventually changing the delivery date of promised orders (repromising). We present a new concept for demand fulfillment in the ATO case which consists of online OP for single orders arriving during the day and DSM once a day, linked in a rolling-horizon scheme. The DSM is based on a mixed integer programming (MIP) model which simultaneously determines assembly and delivery dates for all promised orders. We report on a case study with real data of a computer manufacturer with more than 10,000 orders on hand and 2,000 different components.