## 3 Materials and Methods
### Proposed Adaptive Large Neighborhood Search
#### 3.2.1 Initial Solution
These results lead to the rejection of hypothesis H\({}_{0}\). In conclusion, it is shown that the regression model is statistically significant, meaning that the relationship between fleet size and the number of tardy deliveries is statistically significant and not random. The graphical representation of the tardy deliveries is given in Figure 8.

In problems with 40 customers, when the number of vehicles decreased from 11 to 6, the number of delayed deliveries increased from 0 to 17. In problems with 60 customers, while 27-28 deliveries are not met within time windows with 6 vehicles, all of them could be met on time when the number of vehicles is increased to 12. These results highlight a clear trade-off between fleet size and service quality in terms of on-time deliveries. To investigate this trade-off, a Pareto frontier analysis was performed for each fleet size scenario in the 60-customer problem, and the corresponding visualizations are presented in Figure 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **df** & **SS** & **MS** & **F** & **Significance F** \\ \hline Regression & 1 & 1885.762 & 1885.762 & 475.3121 & 6.6 \(\times\) 10\({}^{-15}\) \\ Residual & 19 & 75.38095 & 3.967419 & & \\ Total & 20 & 1961.143 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: ANOVA results for the regression model between fleet size and number of tardy deliveries in the 60-customer problem set. \begin{table}
\begin{tabular}{c c} \hline \hline
**Regression Statistic** & **Value** \\ \hline Multiple R & 0.980593 \\ R Square & 0.961563 \\ Adjusted R Square & 0.95954 \\ Standard Error & 1.991838 \\ Observations & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Statistical relationship between fleet size and number of tardy deliveries for the 60-customer problems. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Coefficients** & **Standard Error** & **t Stat** & \(p\)**-Value** \\ \hline Intercept & 54.07143 & 2.003659 & 26.98634 & 1.29 \(\times\) 10\({}^{-16}\) \\ \# of Vehicles & \(-\)4.7381 & 0.217327 & \(-\)21.8017 & 6.6 \(\times\) 10\({}^{-15}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Regression coefficients for the relationship between fleet size and tardy deliveries in the 60-customer problem set. Figure 9 shows the Pareto frontier, representing the trade-off between the number of vehicles and tardiness. As the fleet size increases, a significant reduction in tardiness is observed. However, after a certain point--around 10 vehicles in the tested cases--the marginal improvement becomes minimal. According to the trade-off analysis, fleet managers can decide on the appropriate number of vehicles by looking at the trade-offs between solutions. Based on the trade-off curve, fleet managers can make decisions when considering adding more vehicles. This study contributes to the literature on last-mile deliveries with electric vehicles by comparing the effectiveness of traditional cost-oriented route planning approaches with customer-oriented optimization strategies. However, recent literature highlights the uncertain effects of factors such as delivery distance, courier revenue, and task volume on courier availability and coverage rate in crowdsourced door-to-door delivery models [55]. ## 5 Conclusions and Future Works

Today, in terms of last-mile delivery, businesses consider not only operational costs but also customer satisfaction. However, some situations affect the cost, such as the number of vehicles, charging time at stations, number of customers, customer demand, and time window. Such situations cause decision-makers to choose between customer satisfaction and cost. A literature review shows that cost-oriented objective functions such as total distance, energy, travel time, recharging, or operational cost have been studied in EVRPs. On the other hand, it has been noticed that there is a need for studies on minimizing total tardiness, which deals with customer satisfaction.