# Logistics Distribution Vehicle Routing Problem with Time Window under Pallet 3D Loading Constraint
## 2 Problem Description  
The routing problem of delivery vehicles under the three-dimensional pallet loading constraints proposed in this paper needs to consider the three-dimensional constraints of carriages, customer demand, customer service time window, loading and unloading time, and the optimization of distribution routes. In the loading process, due to the difference in the demand of different customers, whether there is enough supporting surface on the top layer of the pallet to support the pallet stacking problem. In the process of route optimization, the distribution cost is higher due to the different service time windows of customer points and the improper distribution order of customer points. A pallet with adjustable support structure height is proposed as the carrier to improve the loading rate and loading and unloading efficiency. It is necessary to effectively integrate distribution resources for reasonable scheduling to reduce the distribution cost. Therefore, we construct a dual-objective model minimizing the distribution cost and maximizing the loading rate to solve the routing optimization problem of distribution vehicles under the constraint of three-dimensional pallet loading. The traditional courier loading process mainly has two ways: The first way is to directly use the sack, which will be attributed to each site of the goods sub-assembly; its advantage is to facilitate the distinction of the goods of each site, but effectively using the limited carriage space is difficult, and the express packaging extrusion can easily break or damage the goods. The second way is to directly stack the goods as regularly as possible in the carriage space. In this way, the carriage space can be effectively used, but without the necessary stack carrier, the loading and unloading process requires more workforce and time, resulting in difficulties in loading and unloading. Compared with the traditional express delivery method, this study introduces the retractable support structure pallet as the express cargo loading and unloading carrier. The study also designs the 3D loading rules to centralize the goods of each distribution site. This unified and orderly operation is not only good at improving the loading and unloading speed of the site, thereby saving cargo distribution time, but can also ensure that the goods are neat and orderly in the distribution process and improve the quality of logistics services. The retractable support structure pallet is used for regular, classified, and uniform stacking of express cargo, as shown in Figure 1. The structure is conducive to flexible height adjustment and stacking regular varying according to the number of cargo. Using a 3D loading constraint algorithm can also further optimize the space utilization of the pallet and vehicle. The specific approach is to differentiate pallets according to different customer nodes. When too many cargoes cause the yarding height to exceed the maximum height limit (the carriage height), the next pallet will be used for cargo loading until the cargo yarding of that customer point is completed. The efficiency of express cargo distribution is influenced by the loading rate of vehicles, cargo loading and unloading speed, and the length of the vehicle distribution path. Under  
Figure 1: Schematic diagram of a retractable 3D pallet. constant vehicle speed, the larger the vehicle loading rate, the faster the cargo loading and unloading speed. Moreover, the shorter the distribution path mileage, the higher the efficiency of vehicle distribution. To this end, this study fully considers the relevant factors to improve vehicle distribution efficiency, introduces height-adjustable 3D pallets for loading cargo, and combines constraints, such as cargo 3D loading space constraints and customer service time window. This study also examines the distribution vehicle path optimization problem with the time window under the 3D loading constraint of pallets.