## 4 Experiments
### Experimental Results and Analysis
#### 4.4.1 Experiment 1  
In order to analyse the solving effect of HCDBAVNS in detail, this paper selects the experimental results of the instance P01 for specific analysis. The information of instance P01 is shown in Tables 6-8.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Supplier** & **X Coordinate** & **Y Coordinate** & \(b_{s}\) & \(c_{s1}\) & \(e_{s1}\) & \(c_{s2}\) & \(e_{s2}\) \\ \hline SUP1 & 99 & 236 & 10 & 1027 & 38 & 1200 & 26 [t] \\ SUP2 & 342 & 29 & 14 & 1072 & 21 & 1079 & 30 \\ SUP3 & 78 & 242 & 14 & 1067 & 24 & 1051 & 36 [b] \\ \hline \end{tabular}
\end{table}
Table 6: Supplier information of P01.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{3}{c}{\(\theta^{1}=W\), \(\theta^{2}=W^{\prime}\), } & \multicolumn{3}{c}{\(\theta^{1}=W\), \(\theta^{2}=W^{\prime}\), } & \multicolumn{3}{c}{\(\theta^{1}=W\), \(\theta^{2}=W^{\prime}\), } \\  & \multicolumn{3}{c}{\(\alpha=0.999\), \(\gamma=0.001\)} & \multicolumn{3}{c}{\(\alpha=0.999\), \(\gamma=0.01\)} & \multicolumn{3}{c}{\(\alpha=0.999\), \(\gamma=0.5\)} \\ \cline{2-10}  & \begin{tabular}{c} **Best** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Average** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Time** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Best** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Average** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Time** \\ **Solution** \\ \end{tabular} & \begin{tabular}{c} **Best** \\ **Solution** \\ \end{tabular} & \
\begin{tabular}{c} **Average** \\ **Solution** \\ \end{tabular} &
\begin{tabular}{c} **Time** \\ **Time** \\ \end{tabular} \\ \hline P01 & **245,399** & **245,399.0** & **4.3** & **245,399** & **245,399.0** & 4.7 & **245,399** & **245,399.0** & 4.6 [t] \\ P06 & **450,664** & **453,527.2** & **45.9** & 452,229 & 453,827.0 & 43.7 & 453,026 & 454,184.4 & **41.6** \\ P11 & **379,602** & **379,602.0** & **14.1** & **379,602** & **379,602.0** & 17.1 & **379,602** & **379,602.0** & 17.3 \\ P16 & **938,095** & **940,699.0** & 59.2 & 939,359 & 941,121.6 & **53.2** & 942,008 & 942,730.2 & 55.7 [b] \\ \hline \end{tabular}
\end{table}
Table 5: The result of instances by HCDBAVNS with different \(\gamma\).  
1. The materials (i.e., MAT1, MAT2,..., MAT10) corresponding to the products needed by all warehouses are supplied by SUP1 and SUP3 without any omission. For the SUP1, the supply quantity of material 1 is 38, and the supply quantity of material 2 is 25, both of which have not exceeded their maximum supply quantities (38 and 26). Similarly, for the SUP3, the supply quantity of material 1 is 23, and the supply quantity of material 2 is 36, both of which have not exceeded their maximum supply quantities (24 and 36) either. It is worth noting that SUP2 is not selected in this best solution because the materials of SUP1 and SUP3 are cheaper than SUP2 and the material supply quantities of SUP1 and SUP3 have met the demand of all warehouses. In addition, SUP2 is further away from the MAN2 and MAN1 than SUP1 and SUP3.  
2. All the products are made by MAN2 and delivered by three vehicles of MAN2. The actual loads of VEH4 are 30, 13, and 18, respectively, all of which have not exceeded their maximum loading capacities (30, 20, and 20). MAN1 is not selected for processing and delivery. Because the unit processing cost of MAN2 is cheaper than that of MAN1, and the position of MAN2 is closer to the SUP1 and SUP3 than MAN2.  
This best solution satisfies the material supply constraint and maximum loading capacity constraint of VRPCSC, that is, it satisfies Formulas (9) and (10), so it is a feasible solution. Thus, HCDBAVNS can effectively solve VRPCSC.