## 3 Problem Setting  
The problem we are considering comprises various elements. To this end, this section describes in detail the characteristics of the assembly process of updating parts, the logistics network, the transports, and the prototype parts. In the life cycle of prototype vehicles, updating parts have to be assembled in a vehicle. The time when updating parts are assembled in the vehicle is decided at short notice and is therefore unknown. In addition, the responsible engineers can pick up individual parts from the internal warehouse for investigations without them being installed in a vehicle. The time of demand from the engineers is also unknown. As soon as a demand for an investigation or for assembly has been received, the parts must be provided as quickly as possible so that the development process is not affected. The aim is to minimize the costs and time for the supply of parts through an optimized allocation concept. Regarding the logistics network, TE-Logistics operates a central hub where all prototype parts for Technical Development are being delivered. The central hub only operates as a receiving point and has no storage capacity for updating parts. The updating parts are ordered by the engineers and delivered by the suppliers. Each part is unique and cannot be reordered. After delivery to the hub, the parts are transshipped to the warehouses. Due to the increasing number of parts, an external warehouse had to be rented on a long-term basis in addition to the internal warehouse, i.e., the network structure cannot be adapted at short notice. Both warehouses have limited capacity and are used exclusively for the storage of updating parts. All incoming parts in the hub are preferably transshipped to the internal warehouse. If the internal warehouse is fully utilized, the parts are transshipped directly to the external warehouse. As the parts are unique, they cannot be stored in both warehouses at the same time. As a result, it is not possible to store all parts in the internal warehouse in the immediate surroundings of the assembly site. If parts from an external warehouse are demanded, they have to be transshipped to the internal warehouse to be picked up by the customer. These transshipments cause high costs and waiting times until customers can pick up the parts. Due to the short-term nature of demands and the necessary quick provision of parts, the transshipments in the prototype logistics cannot be planned in advance, as it can only take place if demands occur. For this reason, it is not possible to consolidate several orders over a longer period of time. The demand for parts from the external warehouse is consolidated for one day before the parts are transshipped. The consolidation of demands for parts from the external warehouse results in waiting times for the assembly or investigation of updating parts, which must be avoided. The task of the logistics planner is to plan the transshipment between the warehouses at short notice in order to provide the demanded parts. All transshipments are carried out by an external logistics service provider (LSP) and are available unlimited at short notice. For each transshipment, fixed transport costs are incurred, depending on the connection between the two warehouses. The transport costs are independent of the utilization of the vehicles. A vehicle with low capacity utilization incurs the same costs as a fully utilized vehicle. All internal transports (hub to internal warehouse) are integrated into a shuttle transport and all transshipments between the internal and external warehouse are carried out pairwise with integrated return transport. If prototype parts are not used for updating prototype vehicles or are no longer required for investigations, they will be scrapped. This can occur if parts have already been further developed with newer versions available with an updated development status and the parts with the older development status have not yet been assembled.