## 6 Results and Analysis
### Experimental Results
In comparison with the 102 routes obtained in the MDTW scenario, but the total travel distance is 41,218 km smaller in this scenario (MDTW). Regarding the assignment of vehicles, Algorithm 2 returned feasible loads as illustrated in Figure 9. Table 8, concentrates the data of 18 vehicles (VIN and height (\(h_{k}\))) before entering the allocation phase. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Auto-Carrier with \(W=10\)**} & \multicolumn{3}{c}{**Auto-Carrier with \(W=11\)**} \\ \hline
**Instance** & **Routes (K)** & **Distance (Km)** & **Time (Min)** & **Routes (K)** & **Distance (Km)** & **Time (Min)** \\ \hline
1 & 4 & 19,263 & 12,660 & 4 & 19,263 & 12,660 \\
2 & 7 & 18,329 & 12,481 & 7 & 18,338 & 12,493 \\
3 & 18 & 71,366 & 48,256 & 14 & 62,571 & 41,809 \\
4 & 24 & 81,429 & 55,950 & 21 & 71,231 & 48,997 \\
5 & 69 & 148,588 & 102,617 & 59 & 130,604 & 87,928 \\
6 & 137 & 323,696 & 213,737 & 118 & 270,872 & 179,242 \\
7 & 195 & 417,909 & 277,747 & 170 & 364,385 & 241,743 \\
8 & 254 & 550,555 & 367,032 & 220 & 471,456 & 312,449 \\
9 & 318 & 681,336 & 458,476 & 278 & 585,245 & 389,968 \\
10 & 366 & 794,553 & 525,284 & 323 & 696,878 & 459,669 \\
11 & 478 & 1,037,633 & 686,562 & 418 & 900,562 & 597,259 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the main dealerships with different auto-carriers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Random Dealerships**} & \multicolumn{3}{c}{**Main Dealerships**} \\ \hline
**Instance** & **Routes (K)** & **Distance (Km)** & **Time (Min)** & **Routes (K)** & **Distance (Km)** & **Time (Min)** \\ \hline
1 & 4 & 17,458 & 11,416 & 5 & 25,649 & 16,875 \\
2 & 10 & 27,626 & 18,854 & 9 & 22,964 & 15,622 \\
3 & 26 & 94,510 & 62,905 & 22 & 91,525 & 61,156 \\
4 & 32 & 111,317 & 75,206 & 37 & 124,226 & 84,035 \\
5 & 95 & 240,376 & 160,016 & 102 & 199,158 & 134,659 From Table 8, Figure 9a shows the output of Algorithm 2 using the auto-carriers of capacity 11 (odd), in which we can observe the allocation of two vans (VIN1, VIN7) using three spaces in both auto-carriers in their platforms, the rest of spaces are occupied by other vehicles. On the other hand, Figure 9b shows the output of the allocation of the vans in auto-carriers of capacity 6. In Table 9 concentrates the results obtained to perform the routing of the demand in the MDTW scenario, using different capacities of auto-carriers and heterogeneous fleet, as it is highlighted in the capacity row of 11 vehicles, this shows the best results as regards distance (km) and time (min), as well as a lower number of auto-carriers (418) employed to carry out the routing of the real demand of the logistics company. A computer with Intel Core i5 [EMAIL_ADDRESS] GHz processor and 16 GB of RAM were used to perform the tests. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**VIN** & **Vehicle \(h_{k}\)** & **VIN** & **Vehicle \(h_{k}\)** \\ \hline
1 & 2.52 m & 10 & 1.47 m \\
2 & 1.47 m & 11 & 1.47 m \\
3 & 1.47 m & 12 & 1.47 m \\
4 & 1.47 m & 13 & 1.47 m \\
5 & 1.47 m & 14 & 1.47 m \\
6 & 1.47 m & 15 & 1.47 m \\
7 & 2.52 m & 16 & 1.47 m \\
8 & 1.87 m & 17 & 1.47 m \\
9 & 1.47 m & 18 & 1.47 m \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Vehicle data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Auto-Carrier (Capacity)** & \multicolumn{3}{c}{**Main Dealerships**} \\ \cline{2-4}  & **Routes (K)** & **Distance (Km)** & **Time (Min)** \\ \hline
3 & 2043 & 4,146,291.8 & 2,720,157 \\
6 & 936 & 2,018,547.9 & 1,332,574 \\
7 & 688 & 1,488,546.3 & 980,416 \\
10 & 478 & 1,037,633.2 & 686,562 \\
**11** & **418** & **900,562.8** & **597,259** \\
3, 6, 7, 10 \& 11 & 660 & 1,416,358.8 & 943,464 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of routing instance 11 with different auto-carriers. Figure 9: Output of vehicles allocation in auto-carriers: (**a**) Odd capacity (**b**) Pair capacity.