# Enhancing E-Grocery-Delivery-Network Resilience with Autonomous Delivery Robots
## 4 Experimentation
### Comparison of Deterministic Model and Chance-Constraint Model  
In the stochastic two-echelon delivery network, the route decision is sensitive to both the travel speed of the vehicles and the deadline requests. We simulated the produced  
\begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{3}{c}{Data Sets} \\ \hline \multicolumn{3}{c}{No. of depots (\(O\)), micro hubs (\(S\)), customers (\(F\)) and vehicles \(K_{un}\), \(K_{ADR}\)} \\ \multicolumn{3}{c}{Small datasets} \\ \multicolumn{3}{c}{Medium datasets} \\ \multicolumn{3}{c}{Depot = 1, micro hub = 1,} & Depot = 1, micro hub = 2, & Depot = 1, micro hub = 4 \\ \multicolumn{3}{c}{ customers = 10} & customers = 50 & Customers = 100 \\ \hline Parameters & Deterministic model/Chance-constraint model \\ Coordination (_Small_) & (20, 20) \\ Coordination (_Medium_) & (100, 100) \\ Coordination (_Large_) & (200, 200) \\ \(n\), \(m\) (Small-scale) & 2, 2 \\ \(n\), \(m\) (Medium-scale) & 4, 10 \\ \(n\), \(m\) (Large-scale) & 10, 20 \\ The average speed \(u^{ban},u^{ADR}\) & \(U\) (1, 6), \(U\) (1, 6) \\ Handling capacity of micro hub & 300 \\ Service deadline of customer \(tl_{f}\) & \(\mu_{\tau_{jk}^{ADR}}+U\) (2, 6) \(\times\) WT + 20 \\ Loading time at a node \(\delta_{f}\) & \(U\) (0.1, 0.5) \(\times\) WT \\ Safety buffer of the battery \(\alpha^{range}\) & \(U\) (1.5, 2.5) \(\times\) WT \\ Maximum operating range of the battery \(\beta^{range}\) & \(\tau_{ijk}^{ADR}+U\) (1.5, 2.5) \(\times\) WT \\ \hline Parameters & Deterministic model & Chance-constraint model \\ Demand of customer \(\zeta_{i}\) & _Lognormal_ (\(\mu_{\zeta_{i}}\), \(\frac{1}{5}\)\(\mu_{\zeta_{i}}\)) & _Lognormal_ (\(\mu_{\zeta_{i}}\), \(\frac{1}{5}\)\(\mu_{\zeta_{i}}\)) considering \\ \multicolumn{3}{c}{\(\varepsilon_{\rho}^{min}\), \(\varepsilon_{\tau}^{ADR}\), \(\varepsilon_{f}\)} \\ Travel time of van \(\rho_{ijk}^{nan}\) & _Lognormal_ (\(\mu_{\rho_{ijk}^{nan}},\frac{UB-\mu_{jjk}^{max}}{100}\)\(\mu_{jjk}^{max}\)) * & _Lognormal_ (\(\mu_{\rho_{ijk}^{nan}},\frac{\varepsilon_{\tau}^{ADR}}{100}\)\(\mu_{jjk}^{max}\) * & _Lognormal_ (\(\mu_{\rho_{ijk}^{nan}},\frac{\varepsilon_{\tau}^{ADR}}{100}\)\(\mu_{jjk}^{max}\) * & _Lognormal_ (\(\tau_{ijk}^{ADR}  
routes under a combination impact of the two parameters in terms of the unmet demand: the travel speed between the ADR and the van, and the service deadline of the customer. We varied the levels of the two parameters and observed the produced results by both the deterministic model and chance-constraint model. Thus, we divided the ratio of the travel speed between the ADR and the van (RSAV) into six levels: 60%, 80%, 100%, 120%, 150% and 200%. The base speed for the van was 10 miles/h (The average speed of a van is lower than the speed traveled in a normal delivery network). The deadline (DL) was set to 40%, 60%, 80%, 100% and 120% of the route length. The base route length was five times the average length of all the links in the network. There were, in total, 30 cases generated in our experiments, which were identified by the combination of two factors with different levels (6 types \(*\) 5 types). To summarize, in this experiment, we experimented with 12 instances, and for each instance we performed 30 cases with various speed ratios and deadlines. Hence, the simulation results were obtained through 360 instances. These instances were tested using both the deterministic model and chance-constraint model under the impact of RSAV and DL (as shown in Table 2). We found that the when the deadlines were tight, for example, 40% to 80% of the route length, the outcome of deterministic model outperformed the chance-constraint model, since the route generated by the deterministic model can mostly arrive on time to serve the demand requested in the beginning. In the situation where the values of the RSAV were small, for example, RSAV60 (60%)-DDL500/CDL500 (100%), and RSAV80 (80%)-DDL500/ CDL500 (100%), the deterministic model and chance-constraint model yielded a higher percentage of unmet demand (Figure 3).