## 2 Optimization Model
### 0-1 Programming Model  
Based on the problem description and assumptions in Section 2.1, a nonlinear 0-1 programming model is constructed to describe ITRTSP. The symbols used in the model and their definitions are shown in Table 2.  
1. Objective function According to the problem description in Section 2.1, the objective function of ITRTSP can be formulated as minimizing the makespan, i.e., \[min[max(EM_{i})-min(SM_{i})],i\in R.\] (1) 2. Transport route constraints \[\sum_{u\in U}x_{i,u}=1,\sum_{d\in D}y_{i,d}=1,i\in R,\] (2) \[x_{i,u},y_{i,d}\in\{0,1\},i\in R,u\in U,d\in D.\] (3)  
Equation (2) indicates that \(i\) can only select one upstream station and one downstream station from U and D, respectively. Equation (3) is variable value constraints for \(x_{i,u}\) and \(y_{i,d}\) \begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Symbol** & **Definition** \\ \hline \multirow{4}{*}{Subscript} & \(i,j\in R\) & Origin number, all cargo from the same origin \(i\) or \(j\) are considered as a whole, referred to as \(i\) or \(j\) \\  & \(u\in U\) & Upstream station number \\  & \(d\in D\) & Downstream station number; \(U\cap D=\Phi\) \\ \hline \multirow{4}{*}{Parameter} & \(q_{i}\) & Quantity of \(i\) \\  & \(SM_{i}\) & Multimodal transport start moment of \(i\) \\  & \(t_{i,u}\) & Road transport time of \(i\) between its origin and \(u\) \\  & \(t_{u,d}\) & Rail transport time between \(u\) and \(d\) \\  & \(t_{d,p}\) & Road transport time between \(d\) and p \\  & \(v_{u}\) & Transshipment efficiency of \(u\) \\  & \(v_{d}\) & Transshipment efficiency of \(d\) \\ \hline \multirow{4}{*}{Basic variable} & \(x_{i,u}\) & 1 if \(i\) select \(u\); 0 otherwise \\  & \(y_{i,d}^{i}\) & 1 if \(i\) select \(d\); 0 otherwise \\  & \(z_{i,j}^{u}\) & 1 if \(i\) is the immediate predecessor activity of \(j\) at \(u\); 0 otherwise \\  & \(h_{i,j}^{d}\) & 1 if \(i\) is the immediate predecessor activity of \(j\) at \(d\); 0 otherwise \\ \hline \multirow{4}{*}{Expand variable} & \(t_{1}^{1}\) & Road transport time for \(i\) between its origin and upstream station \\  & \(t_{2}^{2}\) & Minimal waiting time for \(i\) at its upstream station \\  & \(t_{3}^{4}\) & Loading time for \(i\) at its upstream station \\  & \(t_{4}^{4}\) & Rail transport time for \(i\) between its upstream and downstream station \\  & \(t_{5}^{5}\) & Minimal waiting time for \(i\) at its downstream station \\  & \(t_{i}^{6}\) & Unloading time for \(i\) at its downstream station \\  & \(t_{i}^{7}\) & Road transport time for \(i\) between its downstream station and p \\  & \(AUM_{i}\) & Arrival moment of \(i\) at its upstream station \\  & \(LUSM_{i}\) & The earliest loading start moment of \(i\) at its upstream station \\  & \(ADM_{i}\) & Arrival moment of \(i\) at its downstream station \\  & \(LDSM_{i}\) & The earliest unloading start moment of \(i\) at its downstream station \\  & \(EM_{i}\) & Multimodal transport end moment of \(i\) \\ \hline \end{tabular}
\end{table} 
Table 2: Symbol and definition. (3) Transshipment sequence constraints  
\[z_{i,i}^{u}=0,h_{i,j}^{d}=0,i\in R,u\in U,d\in D, \tag{4}\]  
\[z_{i,j}^{u}\leq x_{i,u},h_{i,j}^{d}\leq y_{i,d},i,j\in R,i\
eq j,u\in U,d\in D, \tag{5}\]  
\[z_{i,j}^{u}\leq x_{j,u},h_{i,j}^{d}\leq y_{j,d},i,j\in R,i\
eq j,u\in U,d\in D, \tag{6}\]  
\[\sum_{i\in R}x_{i,u}=\sum_{i\in R}\sum_{j\in R}z_{i,j}^{u}+1,\sum_{i\in R}y_{i,d}=\sum_{i\in R}\sum_{j\in R}h_{i,j}^{d}+1,u\in U,d\in D, \tag{7}\]  
\[\sum_{i\in R}\sum_{u\in U}z_{i,j}^{u}\leq 1,\sum_{i\in R}\sum_{d\in D}h_{i,j}^ {d}\leq 1,j\in R, \tag{8}\]  
\[\sum_{j\in R}\sum_{u\in U}z_{i,j}^{u}\leq 1,\sum_{j\in R}\sum_{d\in D}h_{i,j}^ {d}\leq 1,i\in R, \tag{9}\]  
\[z_{i,j}^{u},h_{i,j}^{d}\in\{0,1\},i,j\in R,u\in U,d\in D. \tag{10}\]  
Equation (4) indicates no immediate predecessor relationship between \(i\) and itself. Equations (5) and (6) ensure that only when both \(i\) and \(j\) choose \(u\) (or \(d\)) for transshipment can be an immediate predecessor relationship between them.