# A Review of Literature on Vehicle Routing Problems of Last-Mile Delivery in Urban Areas
###### Abstract  
Logistics has long been important in an industrial society. Compared with the traditional structure of distribution, which requires freight to be delivered mostly to warehouses or retail stores, customers now often prefer packages to be delivered to their residences, especially after the delivery challenges during the COVID-19 pandemic. The delivery of parcels to urban residential areas increases the challenge due to the amount of delivery volume, tight delivery schedules, and continuously changing delivery conditions. Last-mile delivery tries to address the challenges, taking advantage of the available automation, sensor and communication technologies, and people's attitudes toward parcel delivery for the benefit of all stakeholders. Various approaches to last-mile delivery have been proposed and analyzed in the literature. This paper reviews the recent literature on vehicle routing for last-mile delivery. The review identified four major categories: crowdshipping, parcel lockers, delivery by sidekicks, and delivery to optional points. The nature of the problems is discussed in five aspects: fleet capacity, time window, fleet option, dynamism of input, and stochastic parameters. The review identifies the achievements and limitations of the research in the areas and proposes a future research agenda. last-mile delivery; vehicle routing; occasional driver; parcel locker; sidekick; optional points of delivery; optimization +
Footnote †: journal: _Sci._  
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Lyft. Sometimes, a logistics company delivers to one of its designated places or parcel locker locations. At the same time, LMD utilizes the help of customers on the demand side; customers are flexible and allow optional delivery locations, one of which will be chosen by the logistics company during delivery planning. Automation certainly helps delivery, and drones have already been commercialized. Sooner or later, autonomous vehicles on the land and water will also be used [1,2]. Amazon commercialized its patented flying warehouses, which also carry small drones [3]. Multiple delivery modes can surely be combined for a delivery job. LMD is the final stage of the parcel delivery process when a customer order is transported from a fulfillment center to a destination, often a residential address [4]. LMD studies discuss diverse issues of delivery [5], including pricing, delivery mode, and security concerns [6]. These studies also investigate innovative solutions, infrastructure setup, staffing, and fleet design in recent years [5,7]. The application of computational intelligence [8], new solution methods [9,10], and the environmental side effects of VRP and LMD [11] are also widely discussed in the literature. Optimization models to employ various types of vehicle in LMD are discussed in [5,12,13]. Researchers have been studying vehicle routing problems (VRPs) to design optimal delivery or pickup routes from one or multiple depots to a number of geographically scattered destinations subject to practical constraints [14,15], playing important roles in logistics [16,17]. Responding to diverse requirements such as working hour limit, fleet capacity, nature of deliverables, and environmental requirements, various VRP models have been discussed, including green VRP and electric VRP. Details of G-VRP [18,19] and E-VRP [20, 21, 22] are discussed in many VRP review papers. Many vehicle routing issues in LMD have long been considered implicitly in conventional VRP [23, 24, 25]. Due to the recent changes in social life, customer behavior, pandemic limitations, increased delivery volume, time pressure, and workforce limitations, e-commerce has widely been accepted by both industry and customers, and the research on vehicle routing for LMD has been pervasively investigated [7,26]. Many papers discuss the vehicle routing issues on LMD considering the new infrastructure of the information and automation technologies [10].