# A Review of Literature on Vehicle Routing Problems of Last-Mile Delivery in Urban Areas
## 4 Literature on LMD Vehicle Routing
### Parcel Lockers  
Parcel lockers, also called pickup points [91], offer a promising solution to some of the challenges posed by LMD for enhanced efficiency, reduced costs, and minimized environmental side effects [92; 93; 94]. In this case, distributors deliver parcels to appropriate lockers and inform the customers. The parcel locker system does not reveal customers' addresses. This system also reduces the risk of parcel damage or loss as customers may not be able to get their products quickly enough [95; 96; 97]. Parcel lockers may also help to reduce emissions [92; 98]. While parcel lockers usually lead to lower shipment costs for customers, people in urban areas are willing to pay more for this service [99; 100]. As shown in Figure 4, the lockers are located in places such as public areas, shopping centers, or residential complexes for customers' convenience. Customers are assigned to parcel lockers, and the vehicle routing is planned. After parcel delivery, recipients receive notifications with locker details and access codes. Recipients visit the locker station and retrieve packages at their convenience. There are different approaches to setting up parcel lockers and assigning customers to them. The lockers can be stationary, temporary, or mobile [101]. The models consider the travel distances of customers as well as those of the fleet. The sizes or other specific technical requirements of the lockers (e.g., refrigerating, chemical restrictions) are commonly considered in the literature. Table 2 details the available literature on the LMD using parcel lockers. Most studies in this category emphasize the significance of capacity constraints for both lockers and fleets [102; 103]. On the contrary, the nature of the parcel locker makes the time windows not as critical as in other cases unless customers specify optional delivery points along with their desired time windows. Multiple fleet options are not discussed extensively in the literature, except for [96], which investigates mobile lockers. Autonomous vehicles and drones can also be considered as fleet options. No research considers the dynamicity; just [104] assumes the stochastic availability of the ODs, in which a combined model of OD and parcel locker are defined. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Ref.** & **Problem Nature** & **Important Considerations** & **Objective(s)** & **Sample Size** & **Solution Method** \\ \hline \multirow{9}{*}{[89]} & & & - & A group of customers is considered a bundle & & & \\  & & & & which can be selected by & & & \\  & & & & ODs to deliver & & & \\  & & & - & Two grouping & & & \\  & & & approaches: clustering, & & & & \\  & - & Dynamically & & corridor creation & & & \\  & - & Capacitated & - & ODs dynamically appear & & & & \\  & & & & at regular time intervals & & & \\  & & & - & Both ODs and fleet have & & & & \\  & & & & limited capacity & & & \\  & & & - & Company should not use & & & \\  & & & & ODs more than its own & & & & \\  & & & & fleet & & & \\ \hline \multirow{9}{*}{[90]} & & & & - & The fleet of other logistic & & & \\  & - & Capacitated & & companies is considered & & & \\ \cline{1-1}  & - & Time & & - & Each vehicle can go on & Minimize the routing & & \\ \cline{1-1}  & - & windowed & & just one round trip & & cost and number of & - & 20 customers & Exact solution (CPLEX) \\ \cline{1-1}  & - & Multiple fleet & - & Each vehicle has limited & & ODs & & \\ \cline{1-1}  & & options & & capacity \& driving time & & & \\ \cline{1-1}  & & & - & Service time is & & & \\ \cline{1-1}  & & & & considered & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._The solution methods vary from heuristic methods and mathematical optimization to simulation-based approaches [92; 93; 94]. Different types of specialized locker for hazardous and perishable items have been suggested [105]. Delivery of a large number of parcels requires big trucks, and lockers are often located in crowded areas; the planning requires consideration of time windows to avoid traffic delays.