## 5 Conclusions and Avenues of Research  
In this study, the eLCVRP-CS-PDS is modeled via a mixed integer linear mathematical model, seeking feasible and good quality routes for light commercial EVs within the goods delivery operation to a fixed number of customers. Due to the charging station installation in order to make the EV routes completion suitable, the effect on the power distribution system is considered from the energy losses standpoint, through a linear power flow formulation supported by an affine constraint. A sensitivity analysis was performed by changing the battery capacity for the two patterns used throughout the routing, the first one accounting for the Capacitated Vehicle Routing Problem and the second one considered the Last Mile Delivery Problem using the shortest path approach. The change in battery capacity provides insights on the quantity and the more convenient location of charging stations along the distribution system that supports the decision maker in the grid future planning according to the current EV battery technology. Additionally, the energy consumed by the EVs and the increase in energy losses compared with the energy losses in the benchmark case were calculated. Other objectives such as the routing cost for the transportation patterns were also considered, reflecting a decrease in this objective as the battery capacity of the EVs was increased. Under this context and considering that there is a variation in energy losses with respect to charging station location, the computational  
Figure 9: Cost of delta in energy losses. experiments show that installing charging stations electrically closer to the substation results in a reduction of the energy losses. This was clearly observed when some of the power network nodes were banned for charging station installation. On the other hand, the newly designed three-index mathematical model within the routing formulation allowed multiple charging stations visits of EVs based on incoming and outgoing freight flow constraints at each node, without the need for using power network nodes copies, which may represent an increase in the computational complexity. The ban of installing charging stations at some power network nodes represents a suitable practice for finding good quality solutions in much less computational times, which can be translated into a heuristic context to obtain an initial solution for the CPLEX solver. Solving large sized-problems and NP-hard nature are still the traditional drawbacks that can be found in the eLCVRP-CS-PDS. Avenues of research may be focused on metaheuristic algorithms and developing heuristic methodologies based on solution space curtailment. With regard to the mathematical model, all of the realistic situations were not considered in this work that can be included in future research, such as multi depot vehicle routing problem, backhauls, and time window constraints. Some final reflections are framed within the realistic approach that suggests independent owners for the power distribution and transportation networks. As depicted throughout this paper, it was assumed that both networks belong to the same owner, as the objective function involves electrical and routing components. Due to the managerial point of view and considering a single owner for both networks, an existing trade-off can be found between the terms in the objective function, contingent upon owner core business. This latter is related to goods transportation and delivery for a logistics company. For a power utility company, the core business is providing energy to homes and industrial customers. However, more utility companies are increasingly integrating logistic activities within their business, encouraging EV sales to logistics companies to increase the recharge of these vehicles by using their power grids. Conceptualization, A.A.-L., W.G.-G., O.D.M. ; Methodology, A. A.-L., W.G.-G., O.D.M. ; Investigation, A.A.-L., W.G.-G., O.D.M. ; Writing--review and editing, A.A.-L., W.G.-G., O.D.M.