## 4 Results
In this manner, for each experiment, with regard to battery capacity Q, there is an increase in the steps of 10 km and 4 km for the EVs in the CVRP and LMDP, respectively. All the experiments were run on a computer with Intel Core i5 2.1 GHz processor (malaysia manufacturing), 8.00 GB of RAM and a 64-bit operative system. The mathematical model was programmed and solved via GAMS/CPLEX interfaced with Matlab for better management on input and output data. Results in Table 1 are shown in the following order: the first and second columns are the battery capacity associated with the EVs for the CVRP and LMDP, respectively. The third column presents the value of each term in the objective function, including the objective function. The routes traveled by the EVs at each travel pattern are presented in  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Cycro [nm]** & **Q.Lump [nm]** & **Coars [USD]** & **Mobility Patterns** & **Routes [Treated]** & **CPII [s]** & **Q.Cycro [nm]** & **Q.Cycro [nm]** & **Consts [USD]** & **Mobility Patterns** & **Routes [Treated]** & **CPII [s]** \\ \hline \multirow{4}{*}{30} & & _F1.482020_ & \multirow{4}{*}{CVRP} & 1-2.45-12.54-13.4-13.  
column five, and the CPU time is shown in the last column for reference. According to the experiments performed in Table 1, the decrease in the objective function value with the increment of battery capacity is notorious. Furthermore, a deeper analysis is required for each term in the objective function. In Figure 2, the routing cost is depicted as a function of the battery capacity. The asterisk tagged in two of the battery capacities in the horizontal axis, represents a ban for installing charging stations at some of the power network nodes, which is explained further in the corresponding cases. Notice that there is a random behavior for routing cost in CVRP, mainly due to the proximity in the spatial distribution of the customers in regards with the power network nodes. Since there is a proximity in the spatial distribution of the customers with respect to power network nodes,  
a reduction in the battery capacity will have a corresponding increase on routing, as the EV requires to detour towards a charging station and retake the path later. Furthermore, this change is not as predictive as for the LMDP vehicles that show a clear tendency to reduce routing cost with an increase in battery capacity. Figure 3 presents the routes performed by the EVs in the CVRP transport pattern, considering a battery capacity of 30 km. Due to the low battery capacity, the final solution requires the installation of charging stations to successfully complete the paths of the EVs. As it was shown in (8) and (9) in the mathematical model, a charging station can be visited multiple times by the EVs. Particularly, this situation is detected in Figure 3, since both EVs visit the same charging station at node 29 belonging the power network. By the other hand, the paths traversed by the EVs in the LMDP transport pattern with a battery capacity of 20 km are shown in Figure 4. Notice that charging station installed at node 24 becomes essential for the routing process as a whole, as it attends three of the five EVs involved in the last mile transport and represents a point strategically located to minimize the energy losses that are increased as the charging process is carried out farther from the electrical substation. It is necessary to mention that the equations assigned for the LMDP allow multiple visits to charging stations from different EVs, which is the situation for two power distribution nodes in the results depicted in Figure 4.  
Figures 5 and 6 show the routes performed with battery capacity of 50 and 28 for the CVRP and LMDP, respectively. The decrease in charging stations installed is observed, compared with the first case.