The part feeding problem at automotive assembly plants deals with the timely supply of parts to the designated stations at the assembly line. According to the just-in-time principle, buffer storages at the line are frequently refilled with parts retrieved from a central storage area. In the industrial application at hand, this is accomplished by means of an internal shuttle system which supplies the various stations with the needed parts based on a given assembly sequence. The main objective is to minimize the required number of shuttle drivers. To solve this inhouse transportation problem, a heuristic solution procedure is developed which is based on the decomposition of the entire planning problem into two stages. First, transportation orders are derived from the given assembly sequence. In the second stage, these orders are assigned to tours of the shuttle system taking transportation capacity restrictions, due dates and tour scheduling constraints into account. Numerical results show that the proposed heuristic solves even large-sized problem instances in short computational time. Benchmark comparisons with Kanban systems reveal the superiority of the proposed predictive part feeding approach.