# Robust Optimization of Transport Organization for China Railway Express
## 3 Optimizing China-Europe Freight Train Logistics Amidst Uncertain Transportation Demand
### A Robust Transformation Model for Uncertain Cargo Transportation Needs  
#### 3.4.1 Uncertain Description of Goods Transportation Demand  
This section focuses solely on the uncertainty surrounding the freight transportation demand at each node, while treating other parameters as deterministic. It is assumed that the transportation demand for goods at each node conforms to a box-type uncertainty set distribution. Specifically, the transport demand at each node is bounded within a symmetric interval. \[Q_{i}=\overline{Q_{i}}\pm\overline{Q_{i}}\cdot\epsilon_{i} \tag{10}\] \begin{table}
\begin{tabular}{c c} \hline \hline Symbol & **Definition** \\ \hline \(N\) & The node set of China–Europe railway network, the element is represented by \(i\), \(N=N_{1}\cup N_{2}\cup N_{3}\) \\ \(N_{1}\) & Collection of domestic nodes of China–Europe railway network \\ \(N_{2}\) & Collection of foreign nodes of China–Europe railway network \\ \(N_{3}\) & China–Europe railway network transit assembly node collection \\ \(A\) & Set of China–Europe railway network paths, index is represented by \((i,j)\) \\ \(V\) & Collection of China–Europe freight trains, indexed by \(v\), \(V=V_{1}\cup V_{2}\) \\ \(V_{1}\) & Domestic section transport train collection \\ \(V_{2}\) & Transnational section transport train collection \\ \hline \hline \end{tabular} \
\begin{tabular}{c c} \hline \hline Symbol & Definition \\ \hline \(\overline{Q_{i}}\) & Container freight demand at transport Node \(i\), unit (TEU) \\ \(\overline{Q_{i}}\) & Average container freight demand at transport node \(i\), units (TEU) \\ \(Q_{v}\) & Capacity, unit (TEU–\(\text{train}^{-1}\)) of Class \(v\) Central European freight train \\ \(C_{v}\) & Fixed cost per train operation of Class \(v\) CEIL, in units (CNY-\(\text{train}^{-1}\)) \\ \(C_{ijv}\) & Class \(v\) China–Europe freight train, unit operating cost between China–Europe network routes, unit (CNY-\(\text{km}^{-1}\)) \\ \(C_{i}^{3}\) & Container unit transfer cost at staging node \(i\), unit (CNY-TEU–\(\text{1}\)) \\ \(\Gamma\) & Robust horizontal adjustment parameters \\ \(\varepsilon_{i}\) & Disturbance level of container freight demand at transport node \(i\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline Symbol & Definition \\ \hline \(f^{p}_{ij}\) & Frequency of Class \(v\) China–Europe freight train on Route \((i,j)\) of China–Europe Railway network, unit (column-week–\(\text{1}\)) \\ \(x^{p}_{ij}\) & Weekly container freight demand of Class \(v\) China–Europe Freight trains on Route \((i,j)\), units (TEU-week–\(\text{1}\)) \\ \(y_{ij}\) & The 0–1 decision variable is 1 if the goods are transported on the China–Europe railway network route \((i,j)\), otherwise 0 \\ \(z_{i}\) & 0–1 decision variable: 1 is selected if the goods are collected at the transit assembly node \(i\) of the China–Europe railway network; 0 is selected otherwise \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameter definition. where \(\overline{Q}_{i}\) represents the average freight demand at node \(i\) and \(\epsilon_{i}\) represents the disturbance level of freight demand at node \(i\). The formulation is given as:  
\[U_{i}=\left[\overline{Q_{i}}-\overline{Q_{i}}\cdot\epsilon_{i},\overline{Q_{i} }+\overline{Q_{i}}\cdot\epsilon_{i}\right] \tag{11}\]  
In the context of robust optimization of transportation paths, \(U_{i}\) denotes the set encompassing demand uncertainties at various nodes. 3.4.2 Robust Optimization Model for China-Europe Freight Train Logistics Amid Uncertain Cargo Demand  
Bertsimas robust optimization, based on robust optimization theory, converts uncertain optimization problems into linear programming problems for simplified resolution. Unlike traditional methods, it adeptly manages uncertainties, yielding high-quality and reliable solutions. Consequently, the [PERSON] robust optimization model is employed in this study to address the optimization challenges within China-Europe freight train logistics amidst uncertain cargo transportation demand.