## 4 Case Study
### Solution of Non-Splittable Model Under Adequate and Insufficient Capacity Scenarios
#### 4.2.2 Transportation Plan (Cargo Flow Path) Results  
In the adequate capacity scenario, the transportation plan from the model (M3) ensures that no cargo flow is split; all express cargo flows are transported directly. The average transportation time for a single express cargo flow is 10:15. In this scenario, the only restriction on path selection from the model (M3) is that the transportation time must not exceed the product's delivery time limit. Table 13 presents part of the transportation plan for the sufficient-capacity scenario. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Express** & **Goods** & **Origin** & **Destination** & **First** & **Delay or** & **Departure** & **Loading** & **Arvival** & **Transport** \\
**Number** & **Category** & **Origin** & **Destination** & **Train** & **Not** & **Time** & **Time** & **Time** & **Time** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 12: Results of train transportation mode selection. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Train Number** & **Capacity-Sufficient Scenario** & **Capacity-Constrained Scenario** \\ \hline \(I_{1}\) & - & High-speed rail confirmation train mode \\ \(I_{2}\) & Passenger train piggyback mode & Reserved mode \\ \(I_{3}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{4}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{5}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{6}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{7}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{8}\) & Passenger train piggyback mode & Reserved mode \\ \(I_{9}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{10}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{11}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ \(I_{12}\) & Passenger train piggyback mode & Passenger train piggyback mode \\ Dedicated train & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Sufficient-capacity scenario model (M3) transportation plan. In the capacity-constrained scenario, based on the constructed non-splittable model, dedicated trains primarily transport low-timeliness products with next-day delivery. Table 14 presents part of the transportation plan for the capacity-constrained scenario, and the remaining part is shown in Appendix A. The distribution of cargo flows in both transportation scenarios is presented in Table 15. Overall, in both scenarios, the express cargo flows were transported without delays or retention issues. In the capacity-sufficient scenario, express shipments achieved full direct transport. However, in the capacity-constrained scenario, the volume of cargo transported by dedicated trains was relatively small. This is because the penalty costs associated with operating dedicated trains were lower than the penalties for delays or retention of the cargo. Consequently, considering the system's overall optimization, the decision was made to operate dedicated express trains.