## 4 Results  
This section describes a newly designed test system to conduct computational numerical experiments and gain insights on the proposed eLCVRP-CS-PDS. The test system is composed of a power distribution system and a transportation network largely used in the specialized literature. The power distribution system corresponds to the 34 nodes three-phase radial test feeder, with a nominal voltage of 24.9 kV, characterized by unbalanced electrical loading, two in-line regulators and shunt capacitors [57]. By the other hand, the transportation network is conformed by the CVRP instance of 19 customers and two vehicles, named in [58] as \(Pn19k2\). Notice in Figure 1 that both power network nodes and customer nodes are placed in the same coordinates system, considering that neither of their nodes match in terms of spatial location. The nodes belonging to the power distribution system are represented by circles joined with a dotted line. Likewise, these nodes are the candidate points for charging station installation. Customers nodes are drawn as solid squares, with node 1 being the depot. In [59], the details of the power distribution system and transportation network used for the computational experiments are presented. Data include: power network topology, lines parameters, electrical loads, equivalence of nodes with set \(V\), nodes coordinates, connectivity matrix between vertices, and CVRP and LMDP features. These latter include the number of vehicles in the CVRP approach and their cargo capacity, and the number of vehicles involved in the LMDP, considering their origin and destination points. It is worth mentioning that nodes of customers in the CVRP are also used by the LMDP to perform the routes to go from origin to destination points. When the vehicle in the LMDP is traveling, it necessarily has to \"touch\" nodes, also used in the CVRP towards the destination, due to the connectivity graph. Both approaches, CVRP and LMDP, are not connected in terms of their routes, i.e., the vehicle used by LMDP does not pick up the merchandise delivered by a vehicle used in the CVRP. A vehicle in the LMDP picks up the parcel in the origin node, left by another transportation mean corresponding to an earlier stage in the chain supply, which is out of the scope of this work. CVRP and LMDP are different approaches that use the same nodes, on the one hand, to meet the demand of the customers (CVRP) and, on the other, to go from origin to destination points (LMDP). Parameters for the numerical experimentation are chosen according to the reality and particular conditions of EV charging. As presented in [60], an output power of 40 kW drawn by a fast charging station requires 25 min to obtain 15.6 kWh to pursue 75 km of driving autonomy, which corresponds to a consistent instantaneous power for the EV charging operation in this work. Additionally, charging duration time at 40 kW can be considered neglectable compared with time required to perform EV routing. Due the nature of the EV charging, this is represented as a constant current load, incorporated accordingly in the power flow equations. The cost associated for charging station installation is around 22,000 USD, including labor, materials, data, connectivity, permit, and taxes, as presented  
Figure 1: Proposed test system for the eLCVRP-CS-PDS: 19 customers and 34 power distribution nodes. in [61]. From the EV operation standpoint, the cost to travel 75 km would be 2.34 USD considering an energy price of 0.15 USD/kWh, which also applies for the energy consumed during the EV charging and energy losses. A cost of 100 USD is estimated to account for the EV maintenance concept every 5000 km traversed. In Table 1, computational results are shown taking into account that the battery driving ranges of the EVs in CVRP and LMDP along the numerical experiments are defined in accordance with their respective transport pattern, considering that the routes performed by the CVRP approach are larger than those presented in LMDP.