# A Memetic Algorithm for an External Depot Production Routing Problem
## 4 Experiments and Results
### Results
The overall cost of storage accounts for 11.39% (100 \(\times\) (11,372.73/99,847.04)) of the overall cost and the cost of vehicle rounds (distribution) accounts for 15.74% (100 \(\times\) (15,715.41/99,847.04)) of the overall cost. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**RL** & **BI** & **SWAP1** & **SWAP2** & **BI \& SWAP2** & **SWAP1 \& SWAP2** & **ALL** & **TOTAL** \\ \hline _Nbr\_BS_ & 2 & 2 & 2 & 7 & 17 & 2 & 32 \\ Percentage & 6.25 & 6.25 & 6.25 & 6.25 & 21.875 & 53.125 & 6.25 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Breakdown of the best solutions by LS. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Instances**} & \multicolumn{2}{c}{**SWAP1**} & \multicolumn{2}{c}{**BI**} & \multicolumn{2}{c}{**SWAP2**} & \multicolumn{2}{c}{**BI\&SWAP2**} & \multicolumn{2}{c}{**SWAP1\&SWAP2**} & \multicolumn{2}{c}{**TOTU**} \\ \hline \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(l\)} & \multirow{2}{*}{\(m\)} & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff & \%Diff \\  & & &  
Tables 18-20 provide details of the comparison of production, storage, and distribution costs, respectively. In Table 18, all production costs obtained with the MA are less than or equal to the production costs of the TPDH. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & \\ \hline \multicolumn{5}{c}{**Best Solutions from MA**} \\ \hline \(n\) & \(l\) & \(m\) & **PROD** & **INV** & **TRANS** & **COST** & **CPU** & **RL** \\ \hline  
I and S2 \\ \hline \multicolumn{5}{c}{ Averages} & \multicolumn{1}{c}{72,758.91} & \multicolumn{1}{c}{11,372.73} & \multicolumn{1}{c}{15,715.41} & \multicolumn{1}{c}{99,847.04} & \multicolumn{1}{c}{280.84} \\ \hline \multicolumn{5}{c}{ rates} & \multicolumn{1}{c}{72.87} & \multicolumn{1}{c}{11.39} & \multicolumn{1}{c}{15.74} & \multicolumn{1}{c}{} & \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Details of the best solutions found in all tests. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & & & & \\ \hline \multicolumn{2}{c}{**Production Cost**} \\ \hline \multicolumn{2}{c}{**Instances**} & \multicolumn{2}{c}{**TPDH**} & \multicolumn{2}{c}{**MA**} \\ \hline \(n\) & \(l\) & \(m\) & **PROD** & **PROD** & **\%Diff** \\ \hline
10 & 3 & 3 & 23,107.50 & 23,107.50 & 0.00 \\
10 & 6 & 2 & 63,082.50 & 57,457.50 & \(-\)8.92 \\
10 & 6 & 3 & 63,082.50 & 57,465.00 & \(-\)8.91 \\
15 & 3 & 2 & 30,712.50 & 30,712.50 & 0.00 \\
15 & 6 & 2 & 82,192.50 & 72,585.00 & \(-\)11.69 \\
15 & 6 & 3 & 82,192.50 & 70,912.50 & \(-\)13.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Comparison of total production costs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Inventory Cost**} \\ \hline \multicolumn{5}{c}{**Instances**} & \multicolumn{2}{c}{**TPDH**} & \multicolumn{2}{c}{**MA**} \\ \hline \(n\) & \(l\) & \(m\) & **INV** & **INV** & \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 19: Comparison of total inventory costs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Production Cost**} \\ \hline \multicolumn{5}{c}{**Instances**} & \multicolumn{2}{c}{**TPDH**} & \multicolumn{2}{c}{**MA**} \\ \hline \(n\) & \(l\) & \(m\) & **PROD** & **PROD** & \\ \hline
20 & 3 & 2 & 35,685.00 & 35,160.00 & \(-1.47\) \\
20 & 3 & 3 & 35,685.00 & 35,685.00 & 0.00 \\  
\hline \hline \multicolumn{5}{c}{**Averages**} & \multicolumn{2}{c}{78,748.59} & \multicolumn{2}{c}{72,758.91} & \(-5.18\) \\ \hline \hline \end{tabular}
\end{table} 
Table 18: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Distribution Cost**} \\ \hline \multicolumn{5}{c}{**Instances**} & \multicolumn{2}{c}{**TPDH(H2)**} & \multicolumn{1}{c}{**MA**} \\ \hline \(n\) & \(l\) & \(m\) & **TRANS** & **TRANS** & **\%Diff** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 20: Comparison of total transportation costs.