# The Electric Vehicle Routing Problem with Time Windows, Partial Readers, and Parcel Lockers
## 1 Introduction  
The COVID-19 pandemic has stimulated the growth of the e-commerce market, which is projected to exceed US$6.388 trillion in 2024 with an annual growth rate of approximately 13.5% [1]. In addition, the number of people who have used online shopping services has significantly increased, reaching 3 billion people in 2018, and this growth has further accelerated due to the challenges of pandemics [2]. Last-mile logistics are a key point for addressing these bottlenecks. However, last-mile activities are costly and environmentally polluting, accounting for 13-75% of overall logistics costs [3]. According to a report by Forum [4], the number of delivery vehicles used is expected to increase by 36%, but effective solutions can lead to a 30% reduction in waste emissions and a nearly 25% decrease in total logistics costs. Logistics companies aim to offer diverse services along with faster deliveries to enhance customer satisfaction and reduce operating costs. Environmental concerns, such as noise and air pollution, prompt them to invest in and implement alternative systems [5]. To effectively address environmental concerns, there is a growing trend to replace fuel-consuming vehicles with those powered by sustainable and renewable energy sources. Electric vehicles (EVs) are widely recognized as one of the cleanest transportation means for both private and commercial purposes that generate no local greenhouse gas (GHG) emissions and help reduce noise pollution. Therefore, logistics companies such as DHL, Amazon, and FedEx have already implemented fleets of EVs into their logistics networks. From the perspective of operation research, the use of EVs in last-mile delivery networks to serve customers is studied by ref. [6], which establishes a more sustainable delivery network. Variants of the electric vehicle routing problem (EVRP) have been developed andextended over the past decade. [PERSON] and [PERSON] [7] investigate recharge policies to tackle the limitations of battery capacities with shorter recharging durations, named the electric vehicle routing problem with time windows and partial recharges (EVRPTW-PR). The conventional last-mile delivery method (i.e., home delivery method) faces various challenges in serving customers within the limitations of time windows and dealing with the possibility of customers being unavailable. Moreover, the problem of urban traffic congestion further causes delays in delivery. These factors contribute to a significant risk of delivery failures, resulting in increased air pollution and logistics costs and decreased customer satisfaction levels. Consequently, logistics companies investigate alternative delivery methods to overcome these challenges. One of the potential alternatives is the self-pickup method, wherein couriers drop customers' parcels at assigned parcel lockers, allowing customers to conveniently retrieve their packages at any time. In practice, parcel locker systems used for delivery have been successfully installed and implemented in more than 20 countries, such as the U.S., UK, Germany, and Canada, which ensure reliable, responsive, and professional delivery experiences [8]. In addition, this delivery method proves particularly suitable during a pandemic as it eliminates the need for direct customer interactions [9]. From the perspective of operations research, we study the integration of parcel lockers into sustainable last-mile delivery networks so as to provide routing plans while minimizing logistics costs, called the electric vehicle routing problem with time windows, partial recharges, and parcel lockers (EVRPTW-PR-PL). While the concept of our study has also been explored by ref. [10], our proposed network differs from them in two features: (1) the locations of parcel lockers and recharging stations (CSs) are distinguished, and (2) each customer is associated only with a designated parcel locker if the self-pickup method is offered. To sum up, our main contributions are highlighted as follows.