# The Electric Vehicle Routing Problem with Time Windows, Partial Readers, and Parcel Lockers
## 2 Related Work
### Electric Vehicle Routing Problems  
The utilization of EVs is first investigated by ref. [6], where they implement a fleet of EVs in a classical VRP. The EVs are assumed to recharge to a minimum of 80% battery capacity with a constant charging rate. The authors devise a mixed-integer non-linear programming model to present the proposed problem. [PERSON] et al. [11] expand upon the initial concept of integrating EVs into VRPs by introducing electric vehicle routing with time windows (EVRPTW). This model assumes that the batteries of EVs are fully charged when they visit recharging stations (CSs), while also considering the time required for recharging. An efficient mixed integer linear programming (MILP) model is provided that can track the battery status of EVs at each visited node. In addition, they generate well-known benchmark instances for EVRPTW, which are widely used in subsequent studies related to EVRPs.  
To analyze the effects of different battery strategies in EVRPTW, [PERSON] and [PERSON] [7] investigate a relaxation of the full recharge policy by allowing partial recharges. This relaxation results in the formulation of a new problem known as the electric vehicle routing problem with time windows and partial recharges (EVRPTW-PR). The research highlights the benefits of the partial recharge policy. To effectively solve EVRPTW with both full and partial recharge policies, [PERSON] et al. [12] propose branch-and-price-and-cut algorithms, which attempt to obtain optimal solutions for these problems. [PERSON] et al. [13] consider a mixed fleet consisting of three vehicle types: EVs, internal combustion vehicles (ICVs), and hybrid vehicles. The research shows that utilizing a mixed fleet can reduce total transportation costs. Furthermore, [PERSON] et al. [14] investigate the use of alternative means such as walking, bikes, and drones for customer service to leverage the time for recharging EVs' batteries.  
To enhance the practicality of routing plans for EVs, many studies consider realistic energy consumption models by providing more accurate estimations of battery charging and discharging rates. [PERSON] and [PERSON] [15] investigate three recharging specifications with varying recharging speeds and costs, and their results reveal tradeoffs between the speeds and costs, which highlight the significant benefits of rapid recharges. [PERSON] and [PERSON] [16] focus on the impacts of load-dependent energy consumption on the EVs' routing plans, where fleet sizes and the current loading of vehicles are load-dependent factors when minimizing total energy consumption. [PERSON] et al. [17] propose a more accurate charging time estimation (i.e., a piecewise linear approximation) to capture charging behavior accurately. [PERSON] et al. [18] offer an arc-based formulation and an exact labeling algorithm to efficiently solve the [17] problem.  
A combination of both electrical and fossil engine vehicles is utilized by refs. [19; 20]. In addition, [PERSON] [21] and [PERSON] et al. [13] investigate the use of hybrid vehicles that switch to consuming fossil fuels when their batteries are fully discharged. Other concepts of EVRPs are extended, such as time-dependent waiting times at public CSs [22; 23], time synchronization at CSs with recharging policies [22; 24; 25], the implementation of battery swapping stations [26; 27; 28], and the impact of traffic on EVs' driving speed [29]. Other applications of electric vehicles (EVs) in goods distribution appear in the survey conducted by ref. [30].