## 4 Experiments
### Experimental Results and Analysis
#### 4.4.2 Experiment 2  
In order to assess the effectiveness HCDBAVNS, this experiment makes a comparison among HCDBAVNS without DCIS (denoted as HDBAVNS), VNS, Particle Swarm Optimization [30] with VNS (denoted as PSOVNS) and HCDBAVNS. This experiment selects 20 instances which have no known optimal solutions. The paper makes some assumptions to get a lower bound for each instance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Item** & **Route** & **Used Capacity** & **Processing Cost** & **Route Distance** & **Transportation Cost** \\ \hline \multirow{6}{*}{The transportation from manufacturers to warehouses} & \multirow{2}{*}{\begin{tabular}{c} VEH4: MAN2– \(>\) \\ STOS\(->\) \\ STO7\(->\) \\ STO2\(->\) \\ STO10\(->\) \\ STO4\(->\) MAN2 \\ \end{tabular} } & \multirow{2}{*}{30} & \multirow{2}{*}{45,360} & \multirow{2}{*}{1301} & \multirow{2}{*}{6505} \\  & & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{2}{*}{30} & \multirow{2}{*}{45,360} & \multirow{2}{*}{1301} & \multirow{2}{*}{6505} \\  & & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{2}{*}{30} & \multirow{2}{*}{45,360} & \multirow{2}{*}{1301} & \multirow{2}{*}{6505} \\  & & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{2}{*}{STO4\(->\) MAN2} & & & & \\ \hline \multicolumn{5}{c}{} \\ \end{tabular} \
\begin{tabular}{c} VEH5: MAN2– \(>\) \\ STO5\(->\) \\ STO1\(->\) \\ STO3\(->\) MAN2 \\ \end{tabular} & \multirow{2}{*}{18} & \multirow{2}{*}{27,216} & \multirow{2}{*}{320} & \multirow{2}{*}{1600} \\  & & & & & \\ \hline \multicolumn{5}{c}{} \\ \end{tabular}
\begin{tabular}{c} Total cost \\ \end{tabular}
\end{table} 
Table 10: The transportation from manufacturers to warehouses in the optimal solution of P01 by HCDBAVNS. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Route Information** & **Route Distance** & **Transportation Cost** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} The transportation from suppliers to manufacturers \\ \end{tabular} } & \multirow{2}{*}{SUP1\(->\) MAN2} & \multirow{2}{*}{384} & \multirow{2}{*}{3840} \\ \cline{1-1} \cline{5-5}  & & & & \\ \hline \multicolumn{5}{c}{} \\ \end{tabular}
\begin{tabular}{c} SUP3– \(>\) MAN2 & 356 & 4984 \\ \hline \multicolumn{5}{c}{} \\ Total cost \\ \end{tabular}
\end{table} 
Table 11: The transportation from suppliers to manufacturers in the optimal solution of P01 by HCDBAVNS. Assuming that the purchase cost of materials can be calculated by the lowest price of materials of all suppliers in the Formula (1), and the lowest purchase cost of materials can be calculated as follows:  
\[Z^{\prime}{}_{\text{PUR}}{=}\sum_{p\in SP}\sum_{l\in SL}o^{\prime}{}_{pl}\min_{s }\{c_{sl}\} \tag{28}\]  
Secondly, in Formula (2), assuming that maximum supply quantities of all suppliers are set to the maximal value of \(e_{sl}\), and the unit delivery costs and distances are a set value between suppliers and manufacturers, then the lowest delivery cost of suppliers' vehicles are shown as follows:  
\[Z^{\prime}{}_{\text{STM}}=2\times\left(\Bigg{[}\sum_{p\in SP}\sum_{l\in SL}o^{ \prime}{}_{pl}/\max(e_{sl})\Bigg{]}\right)\times\min_{s,m}\{d_{sm}\}\times\min_{ s}\{b_{s}\} \tag{29}\]  
Thirdly, assuming the processing cost of materials can be calculated by the lowest processing price of all manufacturers in the Formula (3), and the lowest processing cost can be calculated by Formula (30).