We introduce the driver assignment vehicle routing problem, DAVRP. In this problem, drivers are assigned to customers before demand is known, and after demand is known a routing schedule has to be made such that every driver visits at least a fraction ? of its assigned customers. We present a solution procedure to investigate how much transportation costs increase by adhering to the driver assignments. Furthermore, we distinguish between the case in which customers that are not visited by their assigned driver are visited by backup drivers only, and the case in which slack capacity of regular drivers is utilized to visit these customers. We use randomly generated instances of the DAVRP to provide examples where the difference in transportation costs is substantial.