# Electric-Vehicle Routing Planning Based on the Law of Electric Energy Consumption
## 2 Literature Review  
We present a brief literature review related to EVRPTW-DC in this section. First, the vehicle routing problem (VRP), as the basis of EVRPTW-DC, has been researched for many years. It was originally introduced by [PERSON] and [PERSON] [3] with the aim of minimizing the total transportation cost of visiting a set of customers with known demands by designing proper routes for a fleet of vehicles departing from and returning to the depot. An important extension, VRP with a time window (VRPTW), which considers customers to be served within a specific time range, was then be proposed by [PERSON] [4]. [PERSON] [5] developed another remarkable extension of VRP, named capacitated VRP, which is incorporated with limited cargo capacity of vehicles. Most of the existing work on VRP is constructed on top of these two extensions while using CVs as the transportation tool. However, the increasing negative effects caused by CVs are a heavy burden on the environment. To reduce this burden, green logistics using alternative fuel vehicles, which comprise the second related theme in the literature, has received increasing attention. According to [PERSON]'s survey [6], routing models considering electricity and hydrogen as green alternatives to fossil fuels have been developed in recent years. [PERSON] and [PERSON] [7] proposed a green VRP that considers alternative fuel vehicles with limited driving range and limited refueling infrastructure. This allows vehicles to visit one or more refueling facilities during the route with a fixed refueling time. [PERSON] [8] established a multi-vehicle routing model with quantified environmental costs of noise, air pollution, and fuel consumption. [PERSON] [9] developed a green VRP model to minimize carbon emissions and applied a genetic algorithm to solve the problem. [PERSON] [10] built a hybrid electric vehicle routing model in which vehicles can be powered by either battery or fuel,and designed a maximum neighborhood search algorithm to find the solution. When focusing on EVs as the specific alternative vehicles, the VRP problem is called EVRP. [PERSON] and [PERSON] [11] studied a recharging EVRP in which vehicles have limited range and capacitated load, and the recharging time is assumed to be fixed. The existence of customer time windows was studied to show its influence on the objectives, including the number of employed vehicles and total travel costs. [PERSON] et al. [12] studied the routing problem using a mixed fleet of EVs and CVs, in which EVs were allowed to be recharged during the route and the number of recharging stops was determined by dividing the total traveled distance by the EV's maximum travel range. However, this is unrealistic under actual operation conditions as recharging stations cannot be available everywhere. [PERSON] et al. [13] introduced EVRP with customer time windows and EVs were assumed to follow a linear recharging pattern at a recharging station and always be recharged to full battery capacity. They solved the model by a hybrid variable neighborhood search (VNS) approach combined with a tabu search (TS) heuristic. [PERSON] and [PERSON] [14] proposed a similar model to that of [PERSON] but with a flexible recharging time and the assumption that EVs are allowed to be partially recharged. [PERSON] et al. [15] discussed EVRP under assumptions of multiple charging technologies, and the possibility of partial recharging to strategically reduce the travel time, but without time window consideration. [PERSON] and [PERSON] [16] studied the EVRP with time windows considering both full and partial charging strategies and analyzed the results under both charging strategies. [PERSON] et al. [17] considered a location-routing problem to determine the location of recharging stations and the routing of EVs, and constructed a two-echelon method of tabu search and the Clarke-Wright algorithm to locate recharging stations in the first echelon and determine travel paths of EVs in the second echelon. [PERSON] et al.