## 6 Computational Results and Discussion
### APL Systems  
To enable the experiments to analyze APL systems, six different scenarios for the number of APLs have been defined ranging from \(25\) APLs (scenario \(A1\)) to \(500\) APLs (scenario \(A6\)). For the possible locations of APLs, about \(1500\) nodes have been selected from the given OSM data tagged as residential, ensuring that each APL has a minimum distance  
Figure 8: Comparison of the VKT daily within the districts for the three approaches for estimating the lengths of TSP tours. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **VKT** & **VKT** & **VKT** & **VKT** & **VKT** \\  & **Sum** & **Sum** & **Sum** & **Sweep** & **Savings** \\  & **(Approx.)** & **(TSP)/RAND** & **(TSP)/OSM** & **OSM** & **OSM** \\ \hline H & 2314 & 2735 & 2122 & 1946 & 1982 \\ S1 & 3003 & 3491 & 2685 & 2692 & 2483 \\ S2 & 3540 & 4090 & 3116 & 3236 & 2923 \\ S3 & 4088 & 4687 & 3562 & 3820 & 3344 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of kilometers traveled daily for the approximation approach, the TSP approach, and the two VRP approaches (sweep algorithm and savings algorithm). to all other possible APL locations of 200 m (Figure 9 for the resulting neighborhood structure of the FLP). The resulting structures after solving the underlying FLP with about 10,500 randomly selected customer locations from the OSM data set are illustrated in Figure 10 for all six APL scenarios. In Figure 11, an evaluation of the distances to the APLs is presented. Only 4% of all customers are assigned to an APL within a distance of 300 m for scenario \(A1\) (under the assumption that customers always walk or take a bike to the respective APL). Even in scenario A6 with 500 APLs, only 72% of all customers are assigned to an APL within a distance radius of 300 m. About 66% of the customers are within a radius of 1.5 km to their nearest APL. For all other scenarios, A2 to A6, almost all customers are within that radius, ranging from 97% (A2) to 100% (A5 and A6). Figure 10: Resulting APL locations for all APL scenarios. Figure 9: Neighborhood structure for the FLP. Each APL configuration is further evaluated on the basis of the four given demand scenarios H, S1, S2, and S3. Solving the VRP for all transports from the distribution center (DC) to all APLs leads to the results given in the Appendix A (Table A1). Depending on the capacity of the vehicles \(C\), the numbers of tours are within a range of 46 (H-A1) to 110 tours (S3-A6) for \(C=250\) and 20 to 55 tours for \(C=500\), respectively. The sum of VKT from the DC to the APLs as full truck loads (FTL) and VKT of tours serving more than one APL is typically much smaller than for DD. However, the VKT of customers also needs to be considered when comparing the results for the different scenarios. Following the approach presented with the parameter settings given in Table 1, the DD (the minimum VKT of the respective results of the savings and the sweep algorithm) leads to less VKT for all scenarios for a capacity of the vehicles \(C=250\) (Figure 12). Only for scenarios H-A6 are nearly comparable results achieved with a deviation of about 2%. If the capacity of the vehicles is set to \(C=500\), better results than for direct deliveries are obtained for the APL scenario A6 for all four demand scenarios (Figure 13), ranging from savings in VKT from 21% (H) to 15% (S3), compared to DD given in the Appendix A (Table A2). For demand scenario H, full trucks can only be planned for APL scenarios A1-A3. For scenario A1, the ratio of the distance traveled as full-truck tours is 68%, while for A3 this ratio is only 19%. For the largest demand scenario S3, 87% of the distance for serving APLs is completed as full-truck tours for scenario A1 with 25 APLs, while for scenario A5 this ratio is 7%. In Figure 14, the distances traveled by customers are given, which distinguish the three different options of traveling to the APL. The more APLs are introduced, the lower the total distances for customers are.