## 5 Validation Results
### Results of the Simulation Study
For the URA scenario, even the B shipments are too small, as only highly utilized load units are routed intermodally. In Table 4, we have colored the cells according to their cost-effectiveness, with the green cells representing strongly negative abatement costs--cost savings accompanying emission savings--and the red cells representing positive abatement costs--cost increases associated with emission reductions. In Case 1, abatement costs for X- and Z- shipments are similar, while AC for Y-shipments are still negative, but three times higher. The investigation of the URA scenario for the first case highlights the differences between the dispatching strategies. While the X- and Y-shipments evaluate to similar values, costs for Z-shipments significantly differ from the ARA scenario. If the utilization of load units on the train is focused, the Z shipments cause additional costs for badly utilized fallback road transportation, which impedes higher costs and emissions at a level that raises the abatement cost to a positive value. Comparing the results of Case 1 with Case 2, abatement costs at similar levels are observed. Interestingly, the abatement costs for the Y-shipments of Case 2 are higher in ARA than in URA. Despite the otherwise relatively similar values, the comparison of the cases shows that a generalization of the absolute abatement costs is hardly possible. However, this also shows that the abatement costs do differ between the ABC/XYZ classes, which supports our initial proposition and approach presented in Section 2. \begin{table}
\begin{tabular}{c l|l|c c|c c c c} \hline \hline  & & & \multicolumn{3}{c|}{**Case 1**} & \multicolumn{3}{c}{**Case 2**} \\ \cline{3-8}  & & \(\mathbf{X}\) & \(\mathbf{Y}\) & \(\mathbf{Z}\) & \(\mathbf{X}\) & \(\mathbf{Y}\) & \(\mathbf{Z}\) & \\ \hline \multirow{4}{*}{\(\text{CO}_{2}\)} & \(A\) & & & & \(-874.99\) & \(15.21\) & \(-891.09\) \\  & \(B\) & & & & \(-989.48\) & \(-1169.40\) & \(-1251.47\) \\  & \(n.a.\) & \(-1510.92\) & \(-552.97\) & \(-1411.41\) & & & \\ \hline \multirow{4}{*}{\(\text{CO}_{2}\)} & \(A\) & & & & \(-849.64\) & \(-63.24\) & \(-892.56\) \\  & \(B\) & & & & & & \\ \cline{1-1}  & \(n.a.\) & \(-1514.00\) & \(-513.90\) & \(123.79\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Transportation abatement cost (EUR per mitigated t CO2e) on the ABC/XYZ levels for the evaluated scenarios, with cost savings in green and additional costs in red. To validate the proposition, we examined the results of the simulation runs of the second case study in more detail. Therefore, we conducted Kruskal-Wallis tests for three samples (shipments of the ARA scenario, the URA scenario, and both scenarios combined) and found that there is a significant difference in the abatement costs for at least two inventory groups in all samples. Delving deeper into the pairwise comparisons of the inventory categories' abatement costs, we found that abatement costs between the inventory groups BX-AY, AZ-AY, and AX-AY significantly differ for the ARA and Total samples, and between the AX-AY and AZ-AY groups for the URA sample. The methods used for the tests are described in Appendix C. Results show that, at least across the XYZ inventory groups, abatement costs differ significantly. Investigating the boxplots in Figure A4 shows that abatement costs are highest for the Y-shipments and similar for X and Z shipments. The influence of the ABC dimension was significant only in the ARA and total sample, indicating that the influence of inventory holding costs exists, but is not decisive in most cases. To summarize, the high-level results of the simulated cases and scenarios indicate that abatement costs do pertain to the ABC/XYZ category. Further statistical examination of the second case study showed that there is a significant difference in the abatement costs of some inventory categories. These findings let us conclude that we can partially accept the developed proposition.