# A Memetic Algorithm for an External Depot Production Routing Problem
## 4 Experiments and Results
### Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Inventory Cost**} \\ \hline \multicolumn{2}{c}{**Instances**} & \multicolumn{2}{c}{**TPDH**} & \multicolumn{1}{c}{**MA**} \\ \hline \(n\) & \(l\) & \(m\) & **INV** & **INV** & **\%Diff** \\ \hline \(35\) & 3 & 3 & 4662.75 & 6054.25 & 29.84 \\ \(35\) & 3 & 4 & 4604.25 & 6082.25 & 32.10 \\ \(35\) & 6 & 3 & 21,020.50 & 22,354.25 & 6.34 \\ \(35\) & 6 & 4 & 20,479.50 & 22,402.75 & 9.39 \\ \(40\) & 3 & 3 & 7533.50 & 8387.00 & 11.33 \\ \(40\) & 3 & 4 & 7533.50 & 8334.25 & 10.63 \\ \(40\) & 6 & 3 & 29,374.25 & 34,040.25 & 15.88 \\ \(40\) & 6 & 4 & 28,849.25 & 31,440.50 & 8.98 \\ \(45\) & 3 & 3 & 7550.00 & 9505.00 & 25.89 \\ \(45\) & 3 & 4 & 7874.75 & 9492.50 & 20.54 \\ \(50\) & 3 & 3 & 7767.75 & 9213.00 & 18.61 \\ \(50\) & 3 & 4 & 7767.75 & 9182.50 & 18.21 \\ \hline \hline \multicolumn{6}{c}{**Averages**} & \multicolumn{2}{c}{98,87.34} & 11,372.73 & 15.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 19: _Cont._The costs of production for 16 cases resolved with MA are invariant to the costs of production for TPDH, which corresponds to 50% of the relative results in Table 18. Overall, there is an average decrease of 5.18% in the cost of production obtained with the MA method compared to TPDH. Regarding inventory (storage) cost, there is an increase in the average inventory costs on all instances with an overall average of 9887.34 for the cost obtained with the TPDH method against and a cost of 11,372.73 for the MA. The overall average increase in inventory costs from tests with MA is 15.38% relative to the cost obtained with the TPDH method. Contrary to the inventory costs, a decrease in distribution cost is observed on all results obtained with the MA compared to the costs calculated with the TPDH. We have an overall average of 24,147.83 of the costs with TPDH against an overall average of 15,715.41 of the costs obtained with the MA. The overall average of percentage difference in the distribution cost calculated with the MA compared to the distribution cost calculated with the TPDH is \(-\)35.60%. This reflects an overall average decrease of 35% in the distribution cost obtained with the MA compared to the TPDH. Table 21 shows a comparison of the total cost constituted by the production, inventory and distribution cost obtained with the MA compared to the cost calculated with the TPDH. With an average overall cost of 112,783.76 for TPDH compared to 99,847.04 for MA, there is a decrease ranging from 3.65% to 16.73% on all total costs calculated with MA compared to TPDH with an average overall decrease of 11.07%. With an overall average computation time of 459.51 for TPDH compared to 280.98 for MA, there is an overall average increase of 1485.59% in the computation time for MA compared to TPDH. This is since the average does not consider the relative dispersion of computation times. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Distribution Cost**} \\ \hline  & **Instances** & & **TPDH(H2)** & **MA** & **\%Diff** \\ \hline \(n\) & \(I\) & \(m\) & **TRANS** & **TRANS** & & \\ \hline \(50\) & \(3\) & \(3\) & \(29,310.75\) & \(14,287.50\) & \(-51.26\) \\ \(50\) & \(3\) & \(4\) & \(33,060.00\) & \(16,627.00\) & \(-49.71\) \\ \hline \multicolumn{6}{c}{Averages} & \multicolumn{6}{c}{\(24,147.83\)} & \(15,715.41\) & \(-35.60\) \\ \hline \hline \end{tabular}
\end{table} 
Table 20: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Total Cost**} \\ \hline  & **Instances** & & **TPDH** & & **MA** & & \\ \hline \(\mathbf{N^{0}}\) & \(n\) & \(I\) & \(m\) & **Total Cost** & **CPU** & **Total Cost** & **CPU** & \\ \hline \(1\) & \(10\) & \(3\) & \(2\) & \(34,221.25\) & \(1.53\) & \(30,607.25\) & \(7.00\) & \(-10.56\) & \(357.52\) \\ \(2\) & \(10\) & \(3\) & \(3\) & \(35,826.50\) & \(2.41\) & \(31,303.25  
Figure 2 highlights the effectiveness of MA in reducing the overall cost of production, inventory, and distribution compared to TPDH.