## 3 Establishing a Mathematical Model  
### Symbol Description  
In order to describe the model, the following symbols are defined:  
* indicates the actual traffic network;
* indicates the collection of customer nodes and distribution centers;
* indicates the collection of road segments in route formulation;
* indicates the number of edges between two nodes;
* indicates the set of paths that the arc \((i,j)\) has;
* indicates that one path is selected from the path set \(p_{ij}\);
* indicates the number of vehicles;
* indicates the capacity of one vehicle;
* indicates the load of the vehicle on the arc \((i,j)\);
* indicates the vehicle load in \(P_{ij}^{P}\);
* indicates the demand of the customer node \(i\);
* indicates the travel speed of the vehicle;
* indicates the depreciation cost per vehicle;
* indicates the driver's salary, which is proportional to the driving time;
* indicates the length of the road \(P_{ij}^{P}\);
* indicates the vehicle technical parameters, \(\lambda_{j}=\xi_{j}/k_{j}\psi_{j}\); \(j\in\{1,2\}\);
* indicates the vehicle technical parameters, i.e., the vehicle equipment quality;
* indicates the vehicle technical parameters, where \(Q_{j}=\gamma_{j}\beta_{j}\); \(j\in\{1,2\}\);
* indicates the vehicle technical parameters, where \(v_{j}=\gamma^{\prime}\beta_{j}\); \(j\in\{1,2\}\);
* indicates vehicle technical parameters, where \(\omega_{j}=k_{j}N_{e}^{V}V_{j}\); \(j\in\{1,2\}\);
* indicates the price of fuel per liter;
* indicates the service time of the vehicle at the customer node;
* indicates the travel time from \(i\) to \(j\).
* indicates the time window of the customer, where \(EE_{i}\) is the earliest service time of the vehicle, \(E_{i}\) is the earliest service time of vehicle standard, \(LL_{i}\) is the latest service time for the vehicle, \(L_{i}\) is the latest for the vehicle standard Service time, \(S_{i}\) is vehicle arrival time; if the vehicle arrives at a node i within a range of \((EE_{i},E_{i})\) or \((L_{i},LL_{i})\), it needs to pay the additional cost because of non-compliance  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Parameter** & **Description** & **Value** \\ \hline \multirow{8}{*}{Related parameters of vehicle} & \(K\) & Engine friction coefficient & 0.2 \\  & \(N_{e}\) & Engine speed & 38.33 \\  & \(V\) & Engine displacement & 4.7 \\  & \(A_{f}\) & The area on the front of the vehicle & 5.03 \\  & \(\mu\) & Curb weight of the vehicle & 3850 \\  & \(\varepsilon\) & Vehicle traction efficiency & 0.4 \\  & \(\omega\) & Diesel engine efficiency & 0.9 \\  & \(\phi\) & Road angle & 0 \\ Related parameters of road & \(C_{\gamma}\) & Aerodynamic rotational resistance & 0.01 \\  & \(\xi\) & Diesel heating value & 1 \\  & \(\rho\) & Air density & 1.2041 \\ Others(constant) & \(\psi\) & Conversion factor from gram to liter & 737 \\  & \(g\) & Gravity constant & 9.81 \\  & \(C_{d}\) & Aerodynamic pull & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The comprehensive modal emissions model (CMEM) parameters.  
with the service contract. If the vehicle is serviced before \(EE_{i}\) or after \(LL_{i}\), it will be rejected for exceeding the time allowed by the customer.