## 4 The Methodology for the Proposition Validation
### Total Logistics Cost of Combined Road-Rail Transportation  
Transportation costs generally comprise the cost components of each party involved in relocating goods [49]. Several studies have already defined the cost elements of intermodal transport and the comparison with unimodal transport. We use the cost functions defined in a recent case study on intermodal transportation [58] and detail them with other studies. The authors of [58] elaborate on the costs of intermodal transport services from a consiory's perspective and divide them into several parts. First, the pecunivary cost of transport \(PC\) includes the cost per kilometre and the cost of transshipment. Second, the monetary cost of transit time \(TT\) depends on the transport time, the value of the shipment, and the interest rate. Thirdly, the monetary cost of a delay \(D\) can be quantified, including fines and production downtime costs. Fourth, the cost of cargo loss \(C\) (i.e., damaged, expired, or stolen cargo) is a function of the value of the shipment, the fines, the production downtime costs, and the cost of reordering. Fifth, the study includes the cost of oversized cargo \(OC\), which is highly dependent on the size of the cargo, and sixth, the social cost of transport \(SCT\), the value of which depends on the method of quantification. Additional cost factors that have been considered in other studies are the expenses associated with storing a load unit at a terminal, the cost for the intermodal load units (ILU), incurred either as rent or depreciation, and the management and organization costs [74; 75]. This study focuses on the perspective of the freight owner, which is why the total logistics costs are considered. Therefore, we have decomposed the aspects into six components that reflect the roles of all parties involved, including carriers, hub operators, railway operators, ILU owners, the organizing party, and the freight owner itself, including the transportation cost, order cost, \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} \\ \cline{2-5}  & _Total_ & _Considered_ & _Total_ & _Considered_ \\ \hline Number of suppliers & 36 & 21 & 75 & 8 \\ Number of products & n.a. & n.a. & 359 & 10 \\ Number of shipments & 1215 & 275 & 1706 & 98 \\ Shipment date range & February–December 2021 & February–May 2021 & January–December 2022 & January–December 2022 \\ Transport CHG emissions & 548.51 t & 247.25 t & 305.60 t & 153.01 t \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptive statistics of the two cases under study. Figure 3: A schematic overview of the different dispatching mechanisms in the scenarios (from left to right the ARA, URA, and ARO scenarios). and inventory holding cost. Respectively, these components are the cost for transport operations \(TC\), the cost for hub operations \(HC\), the cost for the ILU rent or depreciation \(ILUC\), the cost for production downtime \(DC\) and the cost for capital \(CC\), as well as the overhead cost for organizing the CRRT \(OC\). \(TC\) includes cost for pre-, main, and post-haulage, and \(HC\) includes the cost of the origin and destination hub. Figure 4 illustrates the occurrence of these components in the transport chain. As the freight owner is the principal of the transport, the costs are borne directly or indirectly by the manufacturing company. As we are missing data on ILU thefts or damages, we neglect these cost components in the focal study. The cost data that was used in the simulation study is a combination of primary data and secondary data:  
* \(TC_{road}\): The input data from case study 1 were used to consider costs for direct truck transport. As a result, we developed a regressive function that depends on the truck utilization \(u\) to determine the freight charges per tonne-kilometre \(TC_{road,direct,htm}\). Specifically, \[TC_{road,direct,htm}(u)=0.0582+\frac{0.0244}{u}\frac{\text{EUR}}{\text{tkm}}\] Additional information on this can be found in Appendix A.