## 3 Methodology
### Notation
#### 3.2.2 Model for Express Cargo
\begin{table}
\begin{tabular}{c c l} \hline \hline
**Type** & **Variable Symbol** & \multicolumn{1}{c}{**Symbol Definition**} \\ \hline  & \(P\) & The set of express, \(p\in P\) \\  & \(\delta_{p}\) & The set of virtual starting points for express \(p\) in spatio-temporal state networks, \(p\in P\) \\  & \(\varepsilon_{p}^{c}\) & The set of virtual endpoints of express \(p\) in spatio-temporal networks, \(p\in P\) \\  & \(\epsilon_{s}^{c}\) & The set of storage nodes in the spatio-temporal network for express \(p\) at station \(s,p\in P,s\in S_{p}\) \\  & \(\hat{\sigma}^{i}\) & The set of dedicated train nodes corresponding to station \(s\) in the spatio-temporal network, \(s\in S_{p}\) \\  & \(B_{p}\) & The set of arcs corresponding to express \(p\) in a spatio-temporal network, \\  & \(p\in P,(s,t,i;s^{\prime},t^{\prime},t^{\prime})\in B_{p},B_{p}=B_{p}^{start}+B_{ p}^{tract}+B_{p}^{lo}+B_{p}^{trans}+B_{p}^{end}+B_{p}^{train}+B_{p}^{train}\) \\  & \(B_{p}^{start}\) & The set of express starting arcs corresponding to express \(p\) in a spatio-temporal network, \(B_{p}^{start}\subset B_{p}\) \\  & \(B_{p}^{travel}\) & The set of express transport arcs corresponding to express \(p\) in a spatio-temporal network, \\ Set Data & \(B_{p}^{travel}\subset B_{p}\) & The set of express loading and unloading arcs corresponding to express \(p\) in a spatio-temporal network, \\  & \(B_{p}^{lo}\subset B_{p}\) & network, \(B_{p}^{lo}\subset B_{p}\) \\  & \(B_{p}^{trans}\) & The set of express transfer arcs corresponding to express \(p\) in a spatio-temporal network, \\  & \(B_{p}^{trans}\subset B_{p}\) & The set of express end arcs corresponding to express \(p\) in a spatio-temporal network, \(B_{p}^{end}\subset B_{p}\) \\  & \(B_{p}^{train}\) & The set of express train arcs corresponding to express \(p\) in a spatio-temporal network, \(B_{p}^{train}\subset B_{p}\) \\  & \(B_{p}^{train}\) & The set of express virtual arcs corresponding to express \(p\) in a spatio-temporal network, \(B_{p}^{train}\subset B_{p}\) \\  & \(N_{p}^{r}\) & The set of express \(p\)-nodes in a spatio-temporal network, \(p\in P\) \\  & \(M\) & The set of goods categories, with values 1, 2, and 3 corresponding to same day delivery, next-day delivery, and three-day delivery, \\  & \(W\) & The set of transport organization modes, with values 1, 2, 3, and 4 corresponding to confirmed, \\  & \(SE_{i}\) & The set of intervals through which train \(i\) passes, \((s,s^{\prime})\in SE_{i}\) \\ \hline  & \(p\) & Express Index \\  & \(m\) & Cargo Category Index \\ Index Data & \(p\) & Index of transport organization modes \\  & \((s,s^{\prime})\) & Interval index \\  & \((s,t,i),(s^{\prime},t^{\prime},t^{\prime})\) & Spatio-temporal network node \\  & \((s,t,i;s^{\prime},t^{\prime},t^{\prime})\) & Spatio-temporal network arc \\ \hline  & \(C_{w}\) & Modes of transport organization \(w\) corresponding to capacity, \(w\in W\) \\  & \(X_{w}\) & Maximum express transport fill rate corresponding to transport organization model \(w\) \\  & \(f_{m}^{a}\) & Modes of transport organization \(w\) corresponding to supply of passenger transport \\  & \(\sigma_{p}^{r}\) & Express \(p^{\prime}\)'s departure station, \(p\in P\) \\  & \(d_{p}\) & Destination station for express \(p\), \(p\in P\) \\  & \(f_{p}^{r}\) & Number of pieces of cargo by express \(p,p\in P\) \\  & \(T_{p=t}^{travel}\) & Departure time of express \(p,p\in P\) \\  & \(M_{p}\) & Classes of goods for express \(p\), \(p\in P\) \\  & \(T^{n}\) & Timeliness of transport of goods of class \(m,m\in M\) \\  & \(f_{train}^{train}\) & Fixed transport revenue per unit of cargo category \(m,m\in M\) \\ Parameter & \(\epsilon_{m}^{train}\) & Flexible transport revenue per unit of cargo category \(m,m\in M\) \\ Data & \(\epsilon_{m}^{travel}\) & Modes of transport organization \(w\) corresponding to unit transport costs \\  & \(e_{m}^{train}\) & Modes of transport organization \(w\) corresponding to unit management costs \\  & \(\epsilon_{m}^{lo}\) & Modes of transport organization \(w\) corresponding to unit loading and unloading costs \\  & \(\epsilon_{m}^{delay}\) & Penalty factor for delays per unit of time \\  & \(e^{init}\) & Penalty coefficients for cargo detention \\  & \(e^{train}\) & Penalty coefficients for specialized transport \\  & & Arc segment durations of arcs \((s,t,i;s^{\prime},t^{\prime},t^{\prime})\) in spatio-temporal networks, \\  & \(T(s,t,i;s^{\prime},t^{\prime},t^{\prime})\) & \(p\in P,(s,t,i;s^{\prime},t^{\prime},t^{\prime})\in B_{p}\), when \(t^{\prime}\geq t,T(s,t,i;s^{\prime},t^{\prime},t^{\prime})=t^{\prime}-t\) and when \\  & \(t^{\prime}<t,T(s,t,i;s^{\prime},t^{\prime},t^{\prime})=t^{\prime}-t+1440\) \\  & \(e^{store}\) & Warehousing costs per unit of express volume per unit of time \\  & \(q\) & Quality of individual expresses \\  & \(h\) & Loading and unloading time per unit of express \\  & \(C^{box}\) & Express consolidation capacity \\ \hline  & \(y^{p}(s,t,i;s^{\prime},t^{\prime},t^{\prime})\) & 0–1 variable, which is 1 if express \(p\) is transported using the arcs \((s,t,i;s^{\prime},t^{\prime},t^{\prime})\) and 0 indicates otherwise, \(\forall p\in P,\forall(s,t,i;s^{\prime},t^{\prime},t^{\prime})\in B_{p}\) \\ Decision Variables & \(Delay^{p}\) & 0–1 variable, which takes the value of 1 if express \(p\) is later than the transport timeframe and 0 indicates otherwise, \(\forall p\in P\) \\  & \(u^{i}_{(s,t^{\prime})}\) & 0–1 variable, which is 1 if train \(i\) undertakes express transport in the interval s \(\rightarrow\) s’; 0 indicates otherwise, \(\forall(s,s^{\prime})\in SE_{i}\). \\  & \(C^{box}\) & For reserved and special train modes, each interval in the operating sector is 1 \\ \hline \hline \end{tabular}
\end{table}