## 6 Case Study
### Results of Reactive and Proactive Approach  
In this section, the results of the proactive approach are presented and compared to the reactive approach. We report the costs, transshipment decisions, and the implications of the sequential planning approach. All periods are solved to optimality in terms of costs. Repeating the case study leads to the same optimal solution. The results of the cost of the case study are summarized in Table 6. We report the overall cost of all 135 periods and the average and standard deviation (\(\mathcal{O}\left(\sigma\right)\)) of the cost per period for the reactive and the proactive approach. Further, we report on the percentage deviation between the reactive and proactive approach. The results from Table 6 show that the proactive approach is more cost-efficient than the reactive approach. An average of 10.5% of costs are saved per period compared to the reactive approach. The representation of the cumulative cost distribution over time is shown in Figure 4.  
The costs in the first periods are the same for the reactive and the proactive approach, as both approaches start with the same initial situation. After a few periods, however, costs are saved in the proactive approach compared to the reactive approach, as the parts are allocated to warehouses with lower approximated future transshipment costs. This leads to lower transshipment costs over all periods. In general, each part has the lowest approximated future transshipment costs in the internal warehouse, as delivery and scrapping are carried out there without transshipment costs. For this reason, the approximated future transshipment costs for each part in the internal warehouse are 0. Therefore, each part should be stored in the internal warehouse if possible. Figure 5 shows the utilization of the internal warehouse over time. It can be seen that the utilization of the internal warehouse increases to almost 100% within a few periods. However, parts with a high probability of being scrapped have lower approximated future transshipment costs in the external warehouse than parts with a high probability of being assembled. For this reason, the model with the proactive approach stores the parts with the highest probability of scrapping in the external warehouse if the capacities of the internal warehouse are fully utilized. Only in the proactive approach, the approximated future transshipment costs are taken into account in the transshipment decision, so that the parts can be transshipped to the optimum warehouse in the first periods. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Transshipment Cost [\(\xi\)]**} & \multicolumn{2}{c}{**Deviation between the Reactive and**} \\ \cline{2-4}  & **Reactive Approach** & **Proactive Approach** & **Proactive Approach [\%]** \\ \hline Over all periods & 33,400 & 29,900 & \\ Average per period \(\mathcal{O}\left(\sigma\right)\) & 247.41 (24.7) & 221.48 (60.3) & \(-\)10.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the cost and the percentage saving in different approaches. Figure 4: Cumulative cost per period. In Figure 6, we have graphically illustrated the proportion of optimally allocated parts per period. We have determined the evaluation of the optimal allocation in a period using a separate optimization model. The sequential approach and the minimization of the approximated future transshipment costs with proactive transshipments have almost achieved the optimal warehouse allocation within the first 10 periods. As no approximated future transshipment costs are used in the reactive approach, the proportion of optimally allocated parts stagnates between 70% and 80%. Figures 5 and 6 thus explain the reduced costs in Figure 4 as soon as the utilization of the internal warehouse increased together with the proportion of optimally allocated parts. Figure 7 shows the number of parts that had to be transshipped to satisfy demand. In the reactive approach, parts had to be transshipped from the external to the internal warehouse in each period.