## 2 Objective Function  
For different transportation organization modes, the corresponding management costs, transportation capacity, and impacts on passenger transportation vary. Considering the trade-offs between management costs, train express capacity, and the impact on passenger transportation, the objective of this model is to maximize the revenue while minimizing the impact on passenger transportation based on the existing high-speed rail passenger train schedules, taking into account the passenger load factor. (1) Passenger Transportation Loss Cost  
High-speed rail express transportation uses high-speed trains primarily serving passenger transportation. This model considers various train transportation organization modes, including dedicated express trains, passenger-assisted modes, reserved modes, and freight-only modes. The reserved mode requires reserving passenger carriages for express cargo, impacting the number of passengers that can be accommodated, and consequently, reducing passenger transportation revenue. Therefore, considering the passenger transportation demand of different trains, the passenger transportation revenue loss under the selected train travel organization mode is determined. The objective function for passenger transportation loss cost is shown in Equation (12). \[minL_{1}=\sum_{i\in I}\left(f_{i}^{ex}-\sum_{w\in W}x_{i}^{w}*f_{w}^{fa} \right)\times e^{pu}\times loss_{i}^{pa} \tag{12}\]  
(2) Dedicated Train Penalty Cost  
Operating a dedicated high-speed rail express train incurs additional penalty costs, which are related to the volume of express cargo transported by the dedicated train. The objective function for the dedicated train penalty cost is shown in Equation (13). \[minL_{2}=\sum_{p\in P}\sum_{(s,t,i)=\delta_{P}\left[s,t,i\varphi,t^{\prime},i^ {\prime}\right]\in B_{p}^{train}}e^{train}\times f_{p}\times q\times y_{p} \left(s,t,i;s^{\prime},t^{\prime},i^{\prime}\right) \tag{13}\]  
3. Constraints  
(1) Transportation Organization Mode Selection Constraint  
To facilitate the convenience of high-speed rail express management and ensure clarity in planning and organization while also reducing the complexity and intersection of loading and unloading operations during transportation, each train can correspond to at most one high-speed rail express transportation organization mode. Equations (14)-(16) indicate that for any train \(i\in I\), the corresponding transportation organization mode \(w\in W\) is unique. Additionally, due to the specific nature of the \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Explanation** \\ \hline \(x_{i}^{w}\) & 0–1 variable, which is 1 if the mode of transport organization of train \(i\) is \(w\) and takes the value 0 \\  & otherwise, where \(i\in I,w\in W\) \\ \(loss_{i}^{pa}\) & 0–1 variable, which indicates the judgement of whether there is a loss of passengers in train \(i\); it is 1 if \\  & there is a loss of passengers in train \(i\) and 0 otherwise, where \(i\in I\) \\ \(v\) & An integer variable indicating the number of specialized high-speed rail train departures \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Decision variables for train travel. transportation time and train schedule, only the first train of the day can choose the high-speed rail confirmation mode for express transportation. \[\sum_{w\in W}x_{i}^{w}\leq 1\ \forall i\in I \tag{14}\]  
\[\sum_{i\in I/\{0\}}x_{i}^{1}=0 \tag{15}\]  
\[\sum_{w\in W/\{1\}}x_{0}^{w}=0 \tag{16}\]  
(2) Passenger Loss Constraint  
For any train \(i\in I\), its seating capacity is influenced by the transportation organization mode it undertakes. Under the reserved mode, train \(i\) may experience passenger loss. Determining whether passenger loss occurs requires comparing the passenger transportation demand of train \(i\) with the passenger transportation capacity that train \(i\) can accommodate under the selected transportation organization mode \(w\).