## 3 Model Formulation
### Parameter and Variables  
To build the model, the following parameters and variables are defined:  
\(M\): Set of candidate transfer stations and distribution center;  
\(M_{1}\): Set of candidate transfer stations;  
\(N_{g}\): Set of customers assigned to transfer station \(g\), and transfer station \(g\);  
\(K\): Set of refrigerated vehicles in the distribution center;  
\(L_{g}\): Set of refrigerated vehicles in the \(g\) transfer station;  
\(d_{ij}\): Distance between \(i\) point and \(j\) point;  
\(v_{1}\): Average speed of refrigerated vehicles in the first-stage route;  
\(v_{2}\): Average speed of refrigerated vehicles in the second-stage route;  
\(g_{i}^{l}\): Service times of vehicle \(l\) for the \(i\)-th customer (or transfer station);  
\(c_{1}\): Use and consumption cost of vehicles per kilometre in the first-stage route;  
\(c_{2}\): Use and consumption cost of vehicles per kilometre in the second-stage route;  
\(c_{1}^{\prime}\): Cost of the driver in the first-stage route;  
\(c_{2}^{\prime}\): Cost of the driver in the second-stage route;  
\(u_{j}^{k}\): Remaining cargo volume of the refrigerated vehicle \(k\) when arriving at the transfer station or the customer point \(j\);  
\(b_{j}^{k}\): Remaining cargo volume of the refrigerated vehicle \(k\) when leaving the transfer station or customer point \(j\);  
\(P_{1}\): Price of unit commodity;  
\(\theta_{1}\): Spoilage rate of product in the transportation process;  
\(\theta_{2}\): Spoilage rate of product in unloading process;  
\(W_{1}\): Fuel consumed in operating the refrigerator during transportation;  
\(W_{2}\): Fuel consumed in refrigerator operation during unloading;  
\(\theta_{3}\): Fuel price per unit weight;  
\(t_{i}^{l}\): Time when the refrigerated vehicle \(l\) reaches point \(i\);  
\(t_{ij}^{l}\): Time required by a refrigerated vehicle \(l\) to travel between two points \(i\) and \(j\);  
\(t_{\text{\text@underline{\tiny{0}}}}^{l}\): Departure time of refrigerated vehicle \(l\) from the transfer station \(g\);  
\(\lambda_{1}\): Transit cost per unit of time;  
\(W_{g}\): Amount of goods transferred at the g transfer station;  
\(v_{3}\): Transfer point unloading processing speed;  
\(q_{i}\): Demand of transfer station \(i\);  
\(q_{i}^{\prime}\): Demand of customer \(i\);  
\(Q_{1}\): Vehicle capacity in the first-stage route;\(Q_{2}\): Vehicle capacity in the second-stage route;  
\(X^{k}_{ij}\) is a 0-1 variable: when \(X^{k}_{ij}=1\), the vehicle \(k\) passes the road between transfer station(or distribution center) \(i\) and transfer station(or distribution center) \(j\); otherwise, \(X^{k}_{ij}=0\);  
\(x^{k}_{j}\) is a 0-1 variable: when \(x^{k}_{j}=1\), the vehicle \(k\) services for customer i; otherwise, \(x^{k}_{j}=0\);  
\(x^{l}_{ijg}\) is a 0-1 variable: when \(x^{l}_{ijg}=1\), the vehicle \(l\) of transfer station \(g\) passes the road between customer (or transfer station ) \(i\) and customer (or transfer station) \(j\); otherwise, \(X^{l}_{ijg}=0\);  
\(Z_{g}\) is a 0-1 variable: when \(Z_{g}=1\), the transfer station \(g\) is used; otherwise, \(Z_{g}=0\);  
\(y^{l}_{ig}\) is a 0-1 variable: when \(y^{l}_{ig}=1\), the vehicle \(l\) of transfer station g provides service for customer \(i\); otherwise, \(y^{l}_{ig}=0\).