## 6 Case Study
### Study Design, Data, and Computational Setup  
This section presents the design of the study and the used data. Furthermore, the sequential planning approach is described. The study is based on historical data to evaluate the proactive transshipment approach with the introduction of demand probabilities. The network for the case study is based on the industrial use case of updating parts of the Volkswagen brand (see Figure 1). The customers \(N^{\text{Customers}}\) are the assembly and scrapping. All parts are delivered to the central hub by the suppliers. However, the hub has no storage capacity. The parts can be transshipped from the hub to either the internal or external warehouse. Both warehouses have a limited storage capacity \(c_{i}^{\text{L}}\) and handling capacity \(c_{i}^{\text{Handling}}\) (see Table 4). All transports are carried out by an external service provider and have unlimited availability. Fixed transshipment costs are incurred for each transport \(R_{ji}^{\text{fix}}\) (see Figure 1). All internal transports (hub to internal warehouse) are integrated into a shuttle transport with further destinations in the Technical Development. All transports between the internal and external warehouse are carried out directly with integrated return transport. The return transport is integrated in the transport costs of Figure 1. A fixed capacity \(c^{V}\) of 1000 parts for all vehicles is assumed. Table 4 shows the storage and handling capacities as well as the allocation of the 38,379 parts that were initially in the logistics network to the warehouses. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Warehouse** & **Capacity [Parts]** & \
\begin{tabular}{c} **Initial Available** \\ **Inventory [Parts]** \\ \end{tabular} &
\begin{tabular}{c} **Handling Capacity** \\ **[Parts]** \\ \end{tabular} \\ \hline
1 (Hub) & 0 & 0 & Unlimited \\
2 (Internal warehouse) & 40,000 & 30,000 & 5000 \\
3 (External warehouse) & Unlimited & 8379 & 5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characterization of the logistics network in the case study. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Precision** & **Recall** & **F1-Score** & **Support** \\ \hline Assembly & 0.88 & 0.84 & 0.86 & 11,215 \\ Scrapping & 0.94 & 0.95 & 0.95 & 28,205 \\ Accuracy & & & 0.92 & 39,420 \\ Macro avg. & 0.91 & 0.90 & 0.90 & 39,420 \\ Weighted avg. & 0.92 & 0.92 & 0.92 & 39,420 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification report of the neural network. For the case study, the orders of a time period of 135 working days from the ERP system are used. Each working day is equal to one period in the model. We depicted the stock at the beginning of the time period and extracted the daily incoming and demanded parts from the ERP system. As this is daily operational planning process and the demands are only available to the planner in the respective period, the periods are solved sequentially. The incoming parts of the respective period are added to the stock \(B_{ix}\) of the hub prior to each new period. We report the total number of demands and incoming parts over all periods and the average and standard deviation (\(\mathcal{O}\left(\sigma\right)\)) per period in Table 5.  
To determine the demand probabilities for calculating the approximated future transshipment costs, the neural network from Section 5 is used sequentially. In each period, the features are generated according to the stock of the current period and are provided to the trained neural network. This generates a demand probability for each part in stock. The proactive approach is compared with the reactive approach. The costs of the reactive approach are also modeled according to the currently implemented transshipment rules. For this purpose, we adapt the previously presented model formulation. The reactive model consists of the objective function (16), the constraints (3)-(9), and (11)-(13), as no demand probabilities are taken into account.