## 6 Results and Analysis  
### Experimental Results  
To evaluate the performance of the auto-carriers routing algorithm with time windows, two scenarios were designed with 11 different instances of the demand, the last instance corresponds to the real problem of the logistics company. The scenarios are the following:  
Figure 8: Vector of auto-carrier capacity: (a) Pair (b) Odd. * _Random Dealerships with Time Windows (RDTW)_--context in which most of the dealerships (34 of 44) were set different time windows for vehicle unloading. * _Main Dealerships with Time Windows (MDTW)_--context that corresponds to the case of the logistics company, only the dealerships (14 of 44) that are located in the main cities of the country establish a time window for the unloading of vehicles. The configuration of the most important parameters for the implementation of the proposed heuristic algorithm is shown in Table 4. Next, the content of the instances is described in Table 5, the first column corresponds to the instance number, the second is the demand size, and in the following columns the content of this in terms of vehicles (cars, partners) and vans (managers). It is necessary to emphasize the number of vans because they use more spaces in the auto-carrier compared to the vehicles. For both scenarios, the same instances demand was used to perform tests and compare the results of the total distance of the generated routes. With the instances of Table 5, a total of 132 tests were made in the two scenarios to the Algorithm 1, as a result of each of the tests the routes were obtained (auto-carriers, each route corresponds to one scenario previously mentioned) and the accommodation of the auto-carrier considering the allocation restrictions, in order to present all the results, these are grouped according to the capacity of the auto-carriers (3, 6, 7, 10, 11, and a heterogeneous fleet with these). Each table shows a comparison of the two scenarios for the eleventh instance, each table contains the column **Routes (K=Auto-carriers)**, this shows the number of routes generated for the eleventh instance, the **Distance (KM)** column contains the cost in terms of kilometers of the routes and the **Time (Min)** column shows the cost in minutes of the same. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline  & **Algorithm 1** \\ \hline mu & 1 \\ alpha & 0.9 \\ lamda & 1 \\ time\_unloading & 15 \\ k & 1 \\ \hline  & **Algorithm 2** \\ \hline initial & 0 \\ \(W_{t}\) & It depends on the auto-carrier K \\ level & \(\frac{W_{t}}{2}\) \\ parity & It depends on the auto-carrier K \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the proposed heuristic algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instance** & **Demand Size** & **Cars** & **Partners** & **Managers** \\ \hline
1 & 20 & 6 & 14 & 0 \\
2 & 50 & 46 & 1 & 3 \\
3 & 100 & 32 & 66 & 2 \\
4 & 200 & 108 & 87 & 5 \\
5 & 500 & 206 & 270 & 24 \\
6 & 1000 & 456 & 502 & 42 \\
7 & 1500 & 654 & 767 & 79 \\
8 & 2000 & 941 & 974 & 85 \\
9 & 2500 & 1164 & 1224 & 112 \\
10 & 3000 & 1433 & 1431 & 136 \\
11 & 3884 & 1810 & 1906 & 168 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test Instances. Table 6 concentrates the results of the routing of the instances using auto-carriers with a capacity 10 and 11 vehicles in the MDTW scenario. The use of capacity auto-carriers 11 obtains a 13% decrease in total distance and total time compared to capacity 10. In addition, 60 less auto-carriers were used to route the demand of the eleventh instance. Algorithm 2 was designed to work with a heterogeneous fleet of auto-carriers, the results of the tests in the two scenarios are shown in Table 7. In this table the results obtained from the tests are compared with the 11 instances in the two scenarios. Sometimes obtaining a smaller number of routes does not guarantee that it is the lowest total distance of the routes, e.g., in the row of instance 5 for the RDTW scenario, 95 routes are generated.