# Logistics Distribution Vehicle Routing Problem with Time Window under Pallet 3D Loading Constraint
## 1 Introduction
[13] combined this problem with path optimization to reduce the number of boxes used. In order to distinguish goods, [PERSON] and [PERSON] [26] and [PERSON] et al. [27] also divided the space into several parts according to the needs of customers, and [PERSON] et al. [28] proposed to use pallelets to plan the customers' needs in the carriage, which, theoretically, is easy to load and unload but still not well enough to discuss the problem of loading and unloading efficiency of a large number of goods. Moreover, since the top support of the pallet is affected by the amount of cargo, [PERSON]'s solution cannot properly balance the high loading rate of the carriage with the function of distinguishing the customer points in the case of the variable amount of cargo at the customer points. From another aspect, combining 3D loading and path optimization considerations plays an important role in the logistics distribution vehicle path problem. [PERSON] et al. [29] proposed the 3 LCVRP model. Subsequently, [PERSON] et al. [30] designed a forbidden search algorithm that integrates the customer's requirements for service time and ultimately produces a higher quality solution based on the study of [29]. [PERSON] and [PERSON] [31] developed a mixed-integer planning model that considered 3D loading constraints and vehicle assignment use and improved the genetic algorithm for solving it. The study was helpful in advancing the vehicle scheduling problem for 3D loading. [PERSON] et al. [32] extend the vehicle routing problem with pickup and distribution to an integrated vehicle routing and loading problem for transportation. Avoid the process of readjusting goods after loading. [PERSON] et al. [27] and [PERSON] et al. [33] solved the vehicle path optimization scheme for multi-cargo types under 3D loading constraints and compared the results with those of classical heuristic algorithms. In [PERSON] and [PERSON]'s study [34], the 3 LCVRP problem is decomposed into a mixture of 93 problems, among which 36 of the best-known results are improved. However, considering the combination of 3D loading and path is difficult, and the current study only considers a relatively small number of cargo types. Furthermore, there are many different sizes of packages in the real courier industry. The customer demand time window is the time interval in which the customer expects the goods to arrive. In the vehicle routing problem with time windows (VRPTW), whether the goods can arrive on time will directly affect the service quality and even the distribution cost [35]. In the design of the time window problem, [PERSON] [36] considered the number of routes, cost, and the importance of time windows to customers and other factors. [PERSON] et al. [37] proposed a hybrid meta-heuristic for multi-objective vehicle routing problems with time windows and considered the workload imbalance in terms of the distances traveled by the used vehicles and their loads. [PERSON] et al. [38] studied the vehicle routing problem of simultaneous pickup and delivery with a time window, constructed a multi-objective mathematical model that minimized distribution cost and vehicle usage, and proposed an effective algorithm based on tabu search to solve the model. [PERSON] et al. [39] then combined the time window problem with carbon emission to promote the research and development of a green supply chain. They take the time window as the optimization criterion and consider various objectives in the routing problem. In the improvement of the time window, [PERSON] [40] used flexible time windows in which vehicles are allowed to serve customers before and after the time window interval. [PERSON] et al. [41] proposed release dates to solve the problem that the time window was not flexible for in-home delivery. [PERSON] et al. [42] proposed that service time is proportional to the units of delivered products, which makes time windows more reasonable. [PERSON] et al. [43] proposed an effective progressive hedging algorithm for vehicle routing problems with two-layer time window assignments.