## 3 Problem Analysis
### Analysis of Decision Variables  
In order to reduce the costs and carbon emissions in the distribution process, we propose a dual distribution model that uses both refrigerated trucks and van-loaded refrigerated containers based on the specific demands of each regional customer point. To determine the most cost-efficient mode of distribution for each customer point, we calculate the costs associated with each option. For example, the total transportation cost for a 1013 km route using a refrigerated truck is RMB 3054, which includes the fixed costs as well as the fuel costs and carbon taxes. The additional costs include the use of reefer boxes, disposable PDF thermometers, refrigerant storage, and vehicle transportation, which total RMB 54.6 per piece of a drug. Based on this calculation, we select refrigerated trucks for transportation when the demand exceeds 56 pieces and vans with refrigerated boxes when the demand is less than or equal to 56 pieces. We set the cost of transporting refrigerated trucks in the region as \(Q_{1}\) and the cost of transporting refrigerated containers in vans as \(Q_{2}\); see Equations (1) and (2), respectively. \[Q_{1}=\sum_{N_{i}=1}^{N}\left(f_{K_{R}}^{n}+f_{K_{R}}\right)+c_{zi}c_{K_{R}} \tag{1}\]  
\[Q_{2}=\sum_{N_{i}=1}^{N}\left(f_{K_{V}}^{n}+f_{K_{V}}\right)+c_{zi}f_{K_{V}}+ x_{zi}\left(f_{C}+f_{P}+f_{K_{f}}\right) \tag{2}\]  
The choice of distribution method is made after calculating the demand cost in the region, and the decision variable \(x_{i}\) is expressed as follows:  
\[T_{i}=\left\{ \begin{matrix}1\,Q_{1}-Q_{2}\geq 0\\ 0\,Q_{1}-Q_{2}<0\end{matrix} \right.\]  
\[x_{i}\text{=}\left\{ \begin{matrix}\text{T}_{i}\text{= 1 Use of refrigerated trucks for distribution}\\ \text{T}_{i}\text{= 0 Use of vans with refrigerated containers}\end{matrix} \right.\]  
The pharmacy number is set to 0, and each customer node is denoted by \(i,j\) (\(i,j\) = 1, 2, 3,..., N). The decision variables \(x_{ij}^{K_{R}}\), \(x_{ij}^{K_{V}}\), \(y_{i}^{K_{R}}\), and \(y_{i}^{K_{V}}\) are denoted as follows:  
\[x_{ij}^{K_{R}}\text{=}\left\{ \begin{array}{l}1\text{ Reef truck travels from customer i to customer j}\\ 0\text{ otherwise}\end{array} \right.\]  
\[x_{ij}^{K_{V}}\text{=}\left\{ \begin{array}{l}1\text{ The van travels from customer i to customer j}\\ 0\text{ otherwise}\end{array} \right.\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Meaning** \\ \hline \(x_{i}\) & Transport mode decision variables \\ \(x_{c}\) & Decision variable for coolant storage amount \\ \(x_{i}\) & Distribution mode selection coefficient: \(T_{i}\) = 1 if use refrigerated trucks for \\  & distribution; \(T_{i}\) = 0 if use refrigerated boxes carried by vans for distribution \\ \(x_{ij}^{K_{R}}\) & Binary variable: equal to 1 if the refrigerated truck was driven from customer \(i\) to \\  & customer \(j\); otherwise 0 \\ \(x_{ij}^{K_{V}}\) & Binary variable: equal to 1 if the van is driven from customer \(i\) to customer \(j\); \\  & otherwise 0 \\ \(y_{i}^{K_{R}}\) & Binary variable: equal to 1 if the requirement of customer \(i\) is fulfilled by refrigerated \\  & car \(K_{R}\); otherwise 0 \\ \(y_{i}^{K_{V}}\) & Binary variable: equal to 1 if the requirement of customer \(I\) is fulfilled by van \(K_{V}\); \\  & otherwise 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Decision variables table. \[y_{i}^{K_{R}} = \left\{ \begin{array}{ll}1\text{ The need of customer i is fulfilled by reefer K}_{R}\\ 0\text{ otherwise}\end{array} \right.\] \[y_{i}^{K_{V}} = \left\{ \begin{array}{ll}1\text{ The need of customer i is fulfilled by van K}_{V}\\ 0\text{ otherwise}\end{array} \right.\]  
Considering the regional and seasonal temperature variance, carrier vans need to place a corresponding quantity of refrigerants. The quantity of refrigerants required is influenced by the annual average and seasonal temperature variations. To clarify this concept, the domestic annual average isotherm map [28] (Figure 2) and the refrigerant storage use table (Table 3) are presented below.