# Logistics Distribution Vehicle Routing Problem with Time Window under Pallet 3D Loading Constraint
## 5 Example Analysis
### Comparative Analysis and Discussion  
This section demonstrates the feasibility of the proposed method. The results are analyzed and commented on the following perspectives: (1) the effectiveness of the proposed algorithm; (2) the superiority of the using pallet. To demonstrate the effectiveness of the proposed method, we undertake a comparative study with [PERSON]'s improved genetic algorithm [31] and simulated annealing (SA) algorithm. The specific experimental data parameters are shown in Table 5.  
As shown in Table 5, the loading rate of the proposed method is 81.68%, only slightly below [PERSON]'s method, but only costs 54.85% of the time taken by [PERSON]'s method. Although the simulated annealing-genetic algorithm can obtain a higher loading rate in a shorter period of time, it is more likely to fall into a local optimum solution. Thus, the average loading rate is affected by the individual lower results and struggles to reach 77.42%. The comparative analysis shows that a hybrid simulated annealing-genetic algorithm can obtain higher loading rate results in a shorter period of time. In addition, to reflect the advantages of using pallets, a comparative analysis between the scheme of the three-dimensional pallet loading and the traditional three-dimensional loading was conducted. The following is the overall scheme discussion of the case. Part of the research results made in this paper mainly includes the optimized loading rate of the path under the three-dimensional pallet loading scheme and the ordinary three-dimensional loading scheme, the time window of violation, the total cost and the target value, as well as the comparison of the two schemes in the unloading time consumed. The number of pallets used has an effect on the loading rate in the carriage (mainly from the independence of the pallets and the volume of the pallets themselves). As shown in Table 6, the average vehicle loading rate of 83.18% for the traditional 3D loading solution is higher than 81.68% for the 3D loading solution using pallets. However, owing to the lack of loading and unloading carriers, a significant amount of time is consumed for loading and unloading work when the node is reached, resulting in an average violation time window of 3.81 h for the former and only 1.43 h for the latter. From the target values, the pallet 3D loading solution is superior to the traditional 3D loading solution  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Hybrid Simulated**} & \multicolumn{2}{c}{**Bortfeldt’s Method**} & \multicolumn{2}{c}{**SA**} \\ \cline{2-7}
**Carriage** & \multicolumn{2}{c}{**Annealing-Genetic Algorithm**} & \multicolumn{2}{c}{**Vehicle Loading**} & \multicolumn{2}{c}{**Vehicle Loading**} & \multicolumn{2}{c}{**Vehicle Loading**} & \multicolumn{2}{c}{**Running Time (h)**} \\ \cline{2-7}
**Number** & **Vehicle Loading** & **Running Time (h)** & **Rate** & **Running Time (h)** & **Rate** & **Running Time (h)** \\ \hline
1 & 82.46\% & 176.11 & 84.78\% & 314.77 & 82.15\% & 175.09 \\
2 & 81.24\% & 233.32 & 80.61\% & 442.02 & 81.07  
when the vehicle loading rates and distribution costs are considered. The unloading times for the two options are compared as follows. As presented in Table 7, the difference in time cost between the pallet loading solution and the 3D loading solution is mainly the time spent on unloading the goods. The 3D loading solution with pallet loading uses a forklift to unload the pallets as a unit to differentiate the customer nodes when unloading the goods, and the time spent is 29.85% of the time spent on traditional 3D loading. By contrast, traditional 3D loading not only takes time to differentiate between customer nodes of goods but also requires manual unloading, which increases the risk of errors in the process.