## 3 Materials and Methods  
### Problem Description  
One of the most important decisions in the delivery process is the routing decisions for deliveries from the warehouse to the customers. The vehicle routing problem (VRP), first scientifically defined by [PERSON] and [PERSON] in 1959, is the problem of determining minimum-cost routes with a fleet of vehicles to meet customer demands. The VRP, one of  
Figure 2: Methods used in EVRP studies. the problems in the NP-hard class, has many different types according to its constraints [35]. The aim of the VRP is to determine routes with minimum cost that meet all customers' demands. There is rich scientific literature on the VRP and its many varieties, which have been studied for about 60 years [35; 36; 37]. A standard VRP is a vehicle routing problem with a loading capacity limit called the Capacitated Vehicle Routing Problem (CVRP). The Capacitated Electric Vehicle Routing Problem (C-EVRP) aims to plan the most suitable routes for customers by considering the energy limitations of electric vehicles and their carrying capacity constraints. Fleet operators calculate the state of charge (SoC) along the routes and plan visits to charging stations to avoid vehicles running out of charge. The use of electric vehicles has also started to gain popularity since the mid-2000s. The demand for electric vehicles has also increased significantly with the spread of \"green logistics\" worldwide [38]. The use of electric vehicles, which have limitations such as limited battery life, high costs, and various charging features in today's technology, causes distribution problems that are different from classical vehicles in fleet size and routing decisions [39]. In particular, battery charging stations are relatively few compared to classic gas stations, and the limited distances allowed by the amount of charge in the battery require that routing decisions for electric vehicles be made with special care. However, electric vehicles are becoming attractive in many different ways [40]. Studies conducted on several companies provide information about how these vehicles are used in freight distribution today. These companies implement a two-stage plan. In the first stage, loads are transported to logistics warehouse centers outside the city with fossil-fuel-burning vehicles. In the second stage, they are distributed to customers within the city using electric vehicles [41]. The EVRP, an important component of distribution systems with a significant share in logistics costs, emerges in different areas of the service sector, such as cargo transportation and automotive, food, and textile sectors where physical production occurs. The basic assumptions of the EVRP are as follows:  
* The demand of each customer is known in advance, and the customer demand cannot be divided (only one vehicle can serve each customer). * The distances between customers and between the warehouse and the customers are fixed and known in advance. * Each vehicle has the same capacity and is ready for service in the warehouse. * Vehicles have a specific battery capacity. The vehicles' state of charge (SoC) should be considered in route planning. * In the case of charging needs, a full or partial charging strategy can be applied from the charging strategies. The Capacity and Time Window Electric Vehicle Routing Problem (CEVRPTW) is a problem that aims to optimize route planning for electric vehicles. Considering the limited battery capacities and charging times of electric vehicles, it is aimed to provide service to customers within the specified time windows. The problem includes constraints such as carrying capacity, locations of charging stations, energy consumption, charging times, and total cost (e.g., distance, time, or energy usage) and plays an important role in developing sustainable transportation solutions. A mathematical model for the Capacity Electric Vehicle Routing Problem with Time Windows (CEVRPTW) was proposed in the literature by [PERSON] et al. (2014) [13].