# The Electric Vehicle Routing Problem with Time Windows, Partial Readers, and Parcel Lockers
## 7 Conclusions  
This paper addresses an extension of EVRPTW-PR by adding the self-pickup method for serving customers. As a result, there are three types of customers considered: (1) home delivery customers, (2) self-pickup customers, and (3) flexible customers. We formulate a mixed-integer programming (MIP) model and develop an ALNS algorithm adopted by ref. [52] for efficiently solving both EVRPTW-PR and EVRPTW-PR-PL instances. Numerical experiments are conducted to test the performance of our proposed ALNS. To provide comprehensive managerial insights regarding the implementation of parcel lockers in delivery networks, we have conducted sensitivity analyses based on the results obtained from EVRPTW-PR and EVRPTW-PR-PL. From our observations, the utilization of parcel lockers can lead to additional cost reductions in serving customers. The extent of cost reduction is influenced by various factors, such as the time windows and locations of customers in each instance. Furthermore, in subset R-1, where customer locations are randomly distributed and wider time windows are provided, we observe a decrease in the number of used vehicles for routing plans. The generality of our algorithm could help tackle other similar problems. For instance, customers' compensation schemes can be investigated by modifying the objective function, which would support policymakers to incentivize customers and enhance delivery network sustainability. Moreover, the cost of allocating parcel locker facilities can be included in the objective function. This provides a more comprehensive model that would help delivery companies make decisions for designing last-mile delivery networks with the use of parcel lockers. However, our research still has some limitations: (1) the scope of the study is limited to analyzing benchmark instances, and no real-world instances have been studied; and (2) the evaluation of the algorithm's performance is challenging due to a lack of results from the existing algorithms or benchmarks for EVRPTW-PR-PL instances. Some potential future research directions are as follows. First, alternative delivery locations and customers' compensation schemes can be investigated to address a more comprehensive delivery network. More specifically, we could add additional costs (i.e., fixed costs for lockers and compensation costs) to the objective function to align with practical businesses. This model would help policymakers decide compensation strategies for more efficient routing plans and enhance customer satisfaction. Second, in realistic scenarios, the impacts of uncertain factors (e.g., travel time and charging/discharging consumption rates) are also worth studying to capture hidden costs within overall delivery costs. This also poses an interesting challenge through the implementation of stochastic programming or robust optimization. Finally, the applicability of our proposed problem can be enhanced by addressing practical delivery networks and offering more managerial insights. Figure 8: Routing plans of (**a**) EVRPTW-PR and (**b**) EVRPTW-PR-PL for instance c101. **Author Contributions:** Conceptualization, V.F.Y. and P.T.A. ; methodology, V.F.Y., P.T.A. and Y.-W.C.; software, P.T.A. and Y.-W.C.; validation, V.F.Y., P.T.A. and Y.-W.C.; formal analysis, Y.-W.C. and P.T.A. ; investigation, P.T.A. and Y.-W.C.; resources, V.F.Y. ; data curation, V.F.Y. and Y.-W.C.; writing--original draft preparation, P.T.A. and Y.-W.C.; writing--review and editing, V.F.Y. ; visualization, P.T.A. ; supervision, V.F.Y. ; project administration, V.F.Y. ; funding acquisition, V.F.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was partially supported by the National Science and Technology Council of the Republic of China (Taiwan) under grant NSTC 111-2410-H-011-020-MY3 and the Center for Cyber-Physical System Innovation from the Featurered Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan.