## 2 Methodology
### Description
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Meaning** & **Unit** \\ \hline \(i\) & \multicolumn{2}{c}{indices} & \\ \(j\) & \multicolumn{2}{c}{The i-th loading point (shovel point), i = 1, 2, 3,..., n} & - (count) \\ \(j\) & \multicolumn{2}{c}{The j-th unloading point (crusher station), j = 1, 2, 3,..., m} & - (count) \\ \(r\) & \multicolumn{2}{c}{The r-th battery-swapping truck, r = 1, 2, 3,..., k} & - (count) \\ \(e\) & \multicolumn{2}{c}{The e-th battery-swapping station, e = 1, 2, 3,..., h} & - (count) \\ \(Q_{c}\) & \multicolumn{2}{c}{Number of available battery-swapping batteries at the e-th swapping station, Q = 1, 2, 3,..., q} & batteries (count) \\ \(x_{ij}\) & \multicolumn{2}{c}{Number of times the r-th battery-swapping truck travels from loading point i to unloading point j} & trips (count) \\ \(y_{ii}\) & \multicolumn{2}{c}{Number of times the r-th battery-swapping truck travels from unloading point j to loading point i} & trips (count) \\ \(d_{ij}\) & \multicolumn{2}{c}{Distance from loading point i to unloading point j} & km \\ \(d_{k}\) & \multicolumn{2}{c}{Distance from unloading point j to the battery-swapping station e} & km \\ \(d_{ai}\) & \multicolumn{2}{c}{Distance from the battery-swapping station e to loading point i} & km \\ \(C_{1r}\) & \multicolumn{2}{c}{Unit distance cost of the r-th battery-swapping truck when fully loaded, r = 1, 2, 3,..., k} & CNY/km \\ \(C_{2r}\) & \multicolumn{2}{c}{Unit distance cost of the r-th battery-swapping truck when empty, r = 1, 2, 3,..., k} & CNY/km \\ \(C_{3r}\) & \multicolumn{2}{c}{Unit distance maintenance cost of the r-th battery-swapping truck, r = 1, 2, 3,..., k} & CNT/km \\ \(E_{1r}\) & \multicolumn{2}{c}{Energy consumption per unit distance when the r-th battery-swapping truck is loaded, r = 1, 2, 3,..., k} & kWh/km \\ \(E_{2r}\) & \multicolumn{2}{c}{Energy consumption per unit distance when the r-th battery-swapping truck is empty, r = 1, 2, 3,..., k} & kWh/km \\ \(K_{r}\) & \multicolumn{2}{c}{Load capacity of the r-th battery-swapping truck, r = 1, 2, 3,..., k} & tons \\ \(E_{r}\) & \multicolumn{2}{c}{Battery capacity of the r-th battery-swapping truck, r = 1, 2, 3,..., k} & kWh \\ \(t\) & \multicolumn{2}{c}{Ambient temperature in the mining area} & \multicolumn{2}{c}{’C} \\ \(t_{0}\) & \multicolumn{2}{c}{Nominal battery capacity at factory temperature} & \multicolumn{2}{c}{\({}^{\circ}\)C} \\ \(k_{o}\) & \multicolumn{2}{c}{Battery capacity fluctuation coefficient with temperature} & \multicolumn{2}{c}{\({}^{\circ}\)\%/\({}^{\circ}\)C} \\ \(N_{i}\)\({}^{min}\) & \multicolumn{2}{c}{Production task requirement of the i-th loading point (shovel point), i = 1, 2, 3,..., n} & tons \\ \(N_{i}\)\({}^{max}\) & \multicolumn{2}{c}{Maximum production capacity of the i-th loading point (shovel point), i = 1, 2, 3,..., n} & tons \\ \(M_{j}\)\({}^{min}\) & \multicolumn{2}{c}{Production task requirement of the j-th unloading point (crusher station), j = 1, 2, 3,..., m} & tons \\ \(V_{1r}\) & \multicolumn{2}{c}{Average speed of the r-th battery-swapping truck when loaded, r = 1, 2, 3,..., k} & km/h \\ \(V_{2r}\) & \multicolumn{2}{c}{Average speed of the r-th battery-swapping truck when empty, r = 1, 2, 3,..., k} & km/h \\ \(T_{init}\) & \multicolumn{2}{c}{Working time per shift} & hours \\ \(T_{o}\) & \multicolumn{2}{c}{Battery charging time at the battery-swapping station} & minutes \\ \(T_{1}\) & \multicolumn{2}{c}{Loading time} & minutes \\ \(T_{2}\) & \multicolumn{2}{c}{Unloading time} & minutes \\ \(T_{2}\) & \multicolumn{2}{c}{Battery-swapping time} & minutes \\ \(z_{ri}\) & \multicolumn{2}{c}{Number of times the r-th battery-swapping truck travels from unloading point j to battery-swapping station e} & trips (count) \\ \(z_{ni}\) & \multicolumn{2}{c}{Number of times the r-th battery-swapping truck travels from battery-swapping station e to loading point i} & trips (count) \\ \(E_{init}\) & \multicolumn{2}{c}{Minimum battery-swapping energy limit coefficient for the truck} & percentage \\ \(E_{r}\)\({}^{now}\) & \multicolumn{2}{c}{Current remaining energy of the r-th battery-swapping truck, r = 1, 2, 3,..., k} & kWh \\ \(E_{r}\)\({}^{start}\) & \multicolumn{2}{c}{Initial battery capacity of the r-th battery-swapping truck, r = 1, 2, 3,..., k} & kWh \\ \(E_{t}\) & \multicolumn{2}{c}{Charging speed of the battery at the battery-swapping station} & kWh/min \\ \hline \hline \end{tabular}
\end{table}