## 2 Research Status and Significance at Home and Abroad
### Model Building
The working cycle is related to the distribution frequency (investment frequency) of express delivery enterprises, and when the total working hours per day are fixed, the length of a single working cycle decreases with the increase of the distribution frequency; \(\bullet\) Decision variables: \(g_{a}\): threshold, that is, \(g_{m}\geq g_{a}\), then \(m\) type packages are classified as bulky, otherwise classified as standard packages; \(x_{tp}\): whether the candidate transit center \(p\) is selected as a \(t\)-type transit center, where \(t=1,2,3\) indicates the standard transit center, the large transit center, and the hybrid transit center, \(x_{tp}\in\{0,1\}\), \(p\in P\); \(y_{ij}^{v2}\): When transporting standard parcels between node \(i\) and node \(j\), vehicle \(v_{2}\) passes through arc \((i,j)\), \((i,j)\in A_{2}\); \(Z_{ij}^{v3}\): When transporting bulky parcels between section \(i\) and node \(j\), vehicle \(v_{3}\) passes through arc \((i,j)\), \((i,j)\in A_{2}\); \(e_{pi}^{e}\): The standard parcel the demand for standard parcels at the end demand point \(i\) is 1 when it is allocated to the transit center \(p\) to serve; otherwise, it is 0; \(e_{pi}^{l}\): The standard parcel the demand for bulky parcels at the end demand point \(i\) is 1 when it is allocated to the transit center \(p\) to serve; otherwise, it is 0; Since the layout of the end-of-line demand point depends on factors such as end-user preferences for mailing and receiving packages, user density, and competitors, it is an external variable, and this article considers it as an established condition. In addition, due to the logistics and distribution within the city, different from trunk line transportation, the distance between the distribution center and the transit center, the transit center and the terminal demand point is limited, generally not exceeding 100 km. For express delivery companies' urban delivery commonly used models, such as Jinbei, Iveco, etc., there is no mileage constraint; time constraint is a key factor for express delivery companies to consider. Therefore, this article uses time constraints rather than vehicle mileage constraints. Based on the above analysis, the following mixed-integer programming model is constructed: \(\text{min}C^{T}=\sum\limits_{p\in P}\left[x_{1p}f_{S}+x_{2p}f_{L}+x_{3p}f_{ MIX}\right]+2\sum\limits_{o,p\in A_{1}}c_{v1}d_{op}(x_{1p}+x_{2p}+x_{3p})+(D_{ Sta}^{Pick}+D_{Sta}^{Ddt})C_{s}+(D_{Ove}^{Pick}+D_{Ove}^{Del})C_{l}\) \(+\sum\limits_{i,j\in A_{2}}c_{v2}d_{ij}y_{ij}^{v2}(x_{1p}+x_{3p})+\sum\limits_{ i,j\in A_{2}}c_{v3}d_{ij}z_{ij}^{v3}(x_{2p}+x_{3p})\) (1) The objective function minimizes the total logistics cost, including the transportation cost from the city distribution center to the transit center, the fixed cost of opening the transit center, the transportation cost from the transit center to the terminal demand point, and the cost of packing the package. \[D_{Sta}^{Pick}=\sum_{i\in Q}\sum_{S_{m}=<S_{a}}D_{i,m}^{Pick}\;D_{Sta}^{Del}=\sum_{ i\in Q}\sum_{S_{m}=<S_{a}}D_{i,m}^{Del} \tag{2}\]  
\[D_{Ove}^{Pick}=\sum_{i\in Q}\sum_{S_{m}=\geq S_{a}}D_{i,m}^{Pick}\;D_{[PERSON]}^{Del}= \sum_{i\in Q}\sum_{S_{m}=\geq S_{a}}D_{i,m}^{Del} \tag{3}\]  
The total number of end demand points. \[\sum_{i\in V_{1}}y_{ij}^{v2}=\sum_{i\in V_{1}}y_{ji}^{v2}= 1\;j\in Q,\;i\
eq j \tag{4}\]  
\[\sum_{i\in V_{1}}z_{ij}^{v3}=\sum_{i\in V_{1}}z_{ij}^{v3}= 1\;j\in Q,\;i\
eq j \tag{5}\]  
Constraints ensure that standard packages and bulky packages at each end demand point are served only once in a cycle and that the number of vehicles coming in at each end demand point is equal to the number of vehicles exiting, both equal to 1. \[t_{i}^{v2}+t_{ij}^{v2}y_{ij}^{v2}\leq T_{v2}\;i,j\in V_{1},i\
eq j,(i\cup j) \cap Q=\varnothing \tag{6}\]  
\[t_{i}^{v3}+t_{ij}^{v3}z_{ij}^{v3}\leq T_{v3}\;i,j\in V_{1},i\
eq j,(i\cup j) \cap Q=\varnothing \tag{7}\]  
Indicates that the travel time on either route does not exceed the working time of the vehicle in a single duty cycle.