# Enhancing E-Grocery-Delivery-Network Resilience with Autonomous Delivery Robots
## 4 Experimentation
### Comparison of Deterministic Model and Chance-Constraint Model
We suspect that this is due to the low speed of ADRs and vans. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **DDL** & **DDL** & **DDL** & **DDL** & **DDL** & **CDL** & **CDL** & **CDL** & **CDL** & **CDL** \\  & **200** & **300** & **400** & **500** & **600** & **200** & **300** & **400** & **500** & **600** \\  & **(40\%)** & **(60\%)** & **(80\%)** & **(100\%)** & **(120\%)** & **(40\%)** & **(60\%)** & **(80\%)** & **(100\%)** & **(120\%)** \\ \hline RSAV60 (60\%) & 18.91 & 17.27 & 16.83 & 14.26 & 9.78 & 18.45 & 16.34 & 16.19 & 14.33 & 11.09 \\ RSAV80 (80\%) & 14.48 & 12.36 & 12.11 & 9.67 & 6.05 & 13.03 & 11.82 & 11.47 & 10.04 & 7.88 \\ RSAV100 (100\%) & 11.22 & 10.56 & 9.86 & 8.08 & 4.40 & 10.92 & 10.20 & 9.53 & 9.01 & 3.85 \\ RSAV120 (120\%) & 8.44 & 6.89 & 5.72 & 4.01 & 0.00 & 8.21 & 6.31 & 5.06 & 4.70 & 0.00 \\ RSAV150 (150\%) & 6.78 & 6.06 & 4.23 & 2.59 & 0.00 & 5.15 & 5.52 & 4.14 & 2.67 & 0.00 \\ RSA200 (200\%) & 4.58 & 4.11 & 3.27 & 1.95 & 0.00 & 4.00 & 3.90 & 2.99 & 2.04 & 0.00 \\ \hline \hline \end{tabular} DDL: deterministic deadline; CDL: chance-constraint deadline.  
\end{table} 
Table 2: Percentage of unmet demand produced by RSAV and DL (%). Figure 3: Percentage of the unmet demand based on different levels of service deadlines. (“D” and “CC” in the legends stand for the deterministic model and chance-constraint model, respectively). The Impact of Confidence Level \(\varepsilon_{\rho}^{cum},\varepsilon_{\tau}^{ADR},and\ \varepsilon_{f}\)  
In this section, we tested the impact of the confidence level on the route decisions, where the deadline and the ratio between the ADR and van was fixed. For example, for one specific network (one instance), we fixed the speed ratio at 100% and the deadline at 80%. In the van-ADR delivery system, we assumed that the ADR was much more reliable than the van, considering the lack of a truck driver and other uncertainties of van deliveries in the network. Thus, we ran the simulation under the chance-constraint model with different values of the confidence level only for \(\varepsilon_{\rho}^{cum},\varepsilon_{f}\), and fixed the \(\varepsilon_{\tau}^{ADR}\). The percentage of unmet demand is shown in Figure 4. Since the service time and demand of the deterministic model follow lognormal distribution, the mean value of the deterministic route was bigger than 0.5 rather than exactly 0.5 (normal distribution). The minimal unmet demand of the deterministic model is achieved when \(\varepsilon_{\rho}^{cum}=0.75,\varepsilon_{f}=0.75\) (marked with orange square). Then, we can generate different routes by changing the confidence level \(\varepsilon_{\rho}^{cum},\varepsilon_{f}\) for the chance-constraint model. We used the same value of confidence level for both \(\varepsilon_{\rho}^{cum},\varepsilon_{f}\). For all the instances that we tested, the minimal percentage of unmet demand corresponding to the confidence level was 1.56, which was also the number we used before in the experimentation. If the confidence level is too big, then all the routes are planned to overpass the deadline (move towards the right end of the confidence level). If the confidence level is too small, then all the routes will be too conservative (move towards the left end of the confidence level).