## 5 Numerical Experiment  
### Scenario Setting  
The Harbin-Dalian high-speed railway connects Harbin City and Dalian City in China, passing through Songyuan City, Changchun City, and Siping City in Jilin Province, as well as Tieling, Liaoyang, Anshan, and Yingkou cities in Liaoning Province, as shown in Figure 5. It passes through three provincial capitals and six prefecture-level cities and is an important transportation artery in the northeast region of China. The Harbin-Dalian high-speed railway is 921 km long with a total of 22 stations. Designed for a speed of 350 km per hour, it is the first high-speed railway that runs through the three provinces of Northeast China. The six cities along the Harbin-Dalian high-speed railway with the highest GDP ranking are Dalian City, Yingkou City, Shenyang City, Harbin City, Anshan City, and Changchun City. The economic situation of cities generally has a positive impact on express delivery demand, and high-speed express delivery stations cannot be arranged for all prefecture-level cities during the planning phase. Therefore, this paper selects Dalian City, Yingkou City, Shenyang City, Harbin City, Anshan City, and Changchun City as the case study objects. The relative distance between some cities along the Harbin-Dalian high-speed railway is shown in Table 3. Three categories of freight flow are analysed: \"same-day delivery\", \"next-morning delivery\" and \"next-day delivery\", which indicate that the product will be transported to the destination within the day, next morning, and the day after tomorrow, respectively. Freight demand by product category for different ODs in different time periods is shown in Table 4. In Table 4, the freight demand for different OD (Origin-Destination) pairs, dispatch time periods, and product types has been subdivided. The time limit requirements for high-speed express delivery services for different product types during different time periods are generally high. In particular, the \"same-day delivery\" product has a short delivery time limit, which imposes certain constraints on the dispatch time domain. As an example, for the downstream direction, the candidate transportation plans for 15 OD pairs among the six cities along the Harbin-Dalian high-speed railway are given. The candidate transportation plan for the Anshan-Harbin is shown in Table 5, and the visualization result is shown in Figure 6. It can be seen that due to the actual number of high-speed trains operating in this section, some feasible paths that meet the relevant constraints contain transfer connections, which increase the capacity of the candidate set and the carrying capacity of high-speed express delivery. For some OD pairs (such as Dalian-Harbin), due to the relatively small number of actual high-speed rail trains and the even distribution of train operating times, feasible alternative transportation path solutions without any transfer are found, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**OD Pair** & **Delivery Time Period** & **Product Type** & **Freight Flow Volume** \\ \hline \multirow{4}{*}{Dalian–Harbin} & 8.00–10.00 & & (159,192,311) \\  & 10.00–13.00 & & (159,192,311) \\  & 13.00–17.00 & & (68,192,311) \\  & 17.00–22.00 & & (68,192,311) \\ \hline \multirow{4}{*}{Anshan–Harbin} & 8.00–10.00 & & (50,61,99) \\  & 10.00–13.00 & & (50,61,99) \\  & 13.00–17.00 & & (21,61,99) \\  & 17.00–22.00 & & (21,61,99) \\ \hline \multirow{4}{*}{Anshan–Shenyang} & 8.00–10.00 & & (424,512,83) \\  & 10.00–13.00 & & (424,512,832) \\ \cline{1-1}  & 13.00–17.00 & & (181,512,832) \\ \cline{1-1}  & 17.00–22.00 & & (181,512,832) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Freight demand by product category for different ODs in different time periods (kg).