In the logistics of prototype parts in the automotive industry, unique parts are stored in warehouses and provided to assembly service providers to ensure a timely assembly of the associated prototype vehicles. As the allocation of the assembly orders to the assembly service providers may change before the start of the assembly, the shipments are planned at short notice. This article considers the short-term task of planning shipments of individual prototype parts from multiple warehouses to multiple assembly service providers. The current literature on planning shipments focuses mainly on parts available in batch sizes larger than one. However, as prototype parts are individual, storing them in adequate warehouses is crucial. A mixed-integer linear programming model for planning transshipments of parts between the warehouses and shipments to the assembly service providers to minimize overall costs is presented. The model enables the utilization of spare capacities of planned transports for a proactive transshipment of parts between warehouses. To this end, the future shipment costs of parts to assembly service providers are approximated to determine suitable warehouses. A numerical study shows that the proactive approach leads to a considerable cost reduction.