# Vehicle Routing Problem with Drones Considering Time Windows and Dynamic Demand
## 2 Related Literature
[39] proposed a novel mathematical formula and a heuristic algorithm based on an Adaptive Large-scale Neighborhood Search algorithm (ALNS) to meet the challenge of path optimization for combined systems. [PERSON] and [PERSON] [40] considered the Energy-constrained Multiple-visit Traveling Salesman Problem (EM-TSPD) of multiple drones at non-customer rendezvous locations, provided a mathematical model for EM-TSPD, and designed a heuristic algorithm to handle medium and large-scale instances. [PERSON] et al. [41] introduced vehicle routing problem with drone (VRPD), taking into account multiple trucks and drones with the aim of minimizing the operation time, and studied the worst-case VRPD. [PERSON] et al. [42] analyzed the operating costs of VRPD and proposed an ALNS for up to 250 customers' questions. [PERSON] et al. [43] and [PERSON] et al. [44] adopted exact algorithms to solve the VRPD model. [PERSON] and [PERSON] [45] provided a hybrid genetic-sweep algorithm to solve the VRPD problem with up to 200 customers' questions. [PERSON] et al. [46] adopted a novel dynamic artificial bee colony algorithm to minimize the overall operating cost in VRPD. [PERSON] et al. [47] extended VRPD to each truck carrying multiple drones to provide service to all customers. [PERSON] et al. [48] established a bi-objective mathematical model for VRPD to minimize delivery completion time and carbon emissions and proposed a non-dominated sorting-based genetic algorithm to solve this problem. Regarding VRPD combined with practical factors, [PERSON] et al. [49] expanded the scope of VRPD research to incorporate a logistics system with two delivery demands: pick-up and delivery. The author introduced an energy consumption model for the drone which overall considers the flying distance of the drone and the weight of the package. They established a mixed integer programming (MIP) model with a problem customization inequality and provided a novel two-stage heuristic algorithm to solve it. [PERSON] et al. [14] considered introducing dynamic demand considerations in VRPD. They suggested that trucks should handle the delivery service for customers who have already placed orders while drones should be employed to replenish any emerging dynamic demands. [PERSON] and [PERSON] [15] explored the issue of dynamic vehicle routing with drones under the same-day delivery scheme and proposed a geographic partition-based approximation of the policy function to determine whether orders should be delivered by drones or vehicles. [PERSON] et al. [50] investigated the extended VRPD problem with customer time windows (VRPDTW) aimed at minimizing travel costs. They also presented a variable neighborhood search (VNS) algorithm that can tackle an instance comprising 50 customers. As mentioned above, the current VRPD research is still in the exploratory stage. A novel vehicle routing problem with drone considering dynamic demands and time windows has yet to be examined. Additionally, the proposed VRPDTWDD proves to be highly practical as it enables each drone to serve multiple customers in a single flight. Lastly, VRPDTWDD considers the impact of the dynamic degree on vehicle scheduling and routing. Recent research findings in this field are summarized in Table 1. Among them, T represents the number of trucks, D represents the number of drones carried on each truck or the number of drones when serving customers independently with the truck, and m is the abbreviation for \"multiple\". SV/MV represents the number of customers per trip (i.e., single visit or multiple visits). Column TW defines whether the problem considers time windows. Column DD defines whether the problem considers dynamic demands.