## 2 Objective Function
#### 3.4.2 Express Cargo Transportation Section  
1. Decision Variables  
The decision variables for the express cargo transportation section of the model are shown in Table 7.  
2. Objective Function  
The model for the express cargo transportation section primarily focuses on optimizing the assembly of express cargo. The objective is to maximize the railway profit from high-speed express delivery while meeting the cargo transportation demand. The aim is to maximize total express cargo revenue and minimize total costs. In this model, the operational costs of high-speed express delivery include transportation costs, management costs, loading and unloading costs, intermediate storage costs, delay costs, and costs \begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & \multicolumn{1}{c}{**Explanation**} \\ \hline \(y^{p}(s,t,i;s^{\prime},t^{\prime},i^{\prime})\) & 0–1 variable, which is 1 if express \(p\) is transported using the arcs \((s,t,i;s^{\prime},t^{\prime},i^{\prime})\) and is 0 otherwise, \\  & where \(\forall p\in P,\forall(s,t,i;s^{\prime},t^{\prime},i^{\prime})\in B_{p}\) \\ \(Delay^{p}\) & 0–1 variable, which takes the value of 1 if express \(p\) is later than the transport timeframe and is 0 otherwise, where \(\forall p\in P\) \\ \(u_{(s,s^{\prime})}^{i}\) & 0–1 variable, which is 1 if train \(i\) undertakes express transport in the interval \(s\to s^{\prime}\) and is 0 otherwise, where \(\forall(s,s^{\prime})\in SE_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Decision variables for express freight transportation. associated with cargo retention. The objective functions for the express cargo transportation section are represented by Equations (21)-(28). (1) Transportation Revenue  
\[maxL_{3}=\sum_{p\in P}\sum_{(s,t,i;s^{\prime},t^{\prime},i^{\prime})\in B^{vir}_{ p}}\big{(}1-y_{p}\big{(}s,t,i;s^{\prime},t^{\prime},i^{\prime}\big{)}\big{)} \left(e^{fixin}_{M_{p}}\times f_{p}+e^{flein}_{M_{p}}\times f_{p}\times q\right) \tag{21}\]  
(2) Operation Cost  
\[minL_{4}=C_{travel}+C_{manage}+C_{load}+C_{trans}+C_{delay}+C_{vir} \tag{22}\]  
1 Transportation Cost  
\[ \begin{array}{c}C_{travel}=\sum\limits_{i\in I}\sum\limits_{(s,s^{\prime}) \in\mathbf{SE}_{i}}\sum\limits_{w\in W}e^{travel}_{w}\times x^{ip}_{i}*u^{i}_{( s,s^{\prime})}\times L_{(s,s^{\prime})}\\ \hskip 14.226378 pt+\sum\
olimits_{\forall(s,s^{\prime})\in\mathbf{SE}}e^{travel }_{A^{\prime}}\times v\times L_{(s,s^{\prime})}\end{array}  \tag{23}\]  
2 Management Cost  
\[C_{manage}=\sum_{i\in I}\sum\limits_{w\in W/\{2/t\}}e^{ma}_{w}\times x^{ip}_{i} +\sum\limits_{p\in P}\sum\limits_{t\in I_{p}}\sum\limits_{(s,t,i;s^{\prime},t ^{\prime},i^{\prime})\in B^{vir}_{p}}e^{ma}_{\
eq 2^{\prime}}\times x^{ip^{ \prime}2^{\prime}}\times f_{p}\times q\times y_{p}\big{(}s,t,i;s^{\prime},t^{ \prime},i^{\prime}\big{)}/2+e^{ma}_{\
eq A^{\prime}}\times v \tag{24}\]  
3 Loading and Unloading Cost  
\[ \begin{array}{c}C_{load}=\sum\limits_{p\in P}\sum\limits_{w\in W}\sum \limits_{(s,t,i;s^{\prime},t^{\prime},i^{\prime})\in B^{vir}_{p}}e^{lo}_{w} \times x^{ip}_{i}\times f_{p}\times q\times y_{p}(s,t,i;s^{\prime},t^{\prime},i^{\prime})/2\\ \hskip 14.226378 pt+\sum\limits_{p\in P}\sum\limits_{(s,t,i)=g_{p};(s,t,i;s^{ \prime},t^{\prime},i^{\prime})\in B^{vir}_{p}}e^{lo}_{\
eq A^{\prime}}\times f _{p}\times q\times y_{p}(s,t,i;s^{\prime},t^{\prime},i^{\prime})\end{array}  \tag{25}\]  
4 Transfer and Storage Cost  
\[C_{trans}=\sum_{p\in P}\sum\limits_{(s,t,i;s^{\prime},t^{\prime},i^{\prime}) \in B^{vir}_{p}}e^{store}\times T\big{(}s,t,i;s^{\prime},t^{\prime},i^{\prime} \big{)}\times f_{p}\times q\times y_{p}\big{(}s,t,i;s^{\prime},t^{\prime},i^{ \prime}\big{)} \tag{26}\]  
5 Delay Cost  
\[