# Robot Routing Problem of Last-Mile Delivery in Indoor Environments
## 5 Experimental Results
### Illustrative Example  
In this research, the illustrative example was based on an actual university building containing six floors, as shown in Figure 7a. Among the many rooms in the building, twelve rooms were selected as the demand nodes (i.e., customers). Figure 7b shows the indoor layout of the first floor of the building, and the remaining floors exhibit almost the same layout. We assumed that the robots have an exact indoor map and know how many corners there are. Figure 6: Overall procedure of the proposed heuristic approach. To generate demand information for this example, each demand node exhibited a nonnegative delivery demand (i.e., the number of parcels) that was randomly generated to attain a value of one or two. Additionally, the distance between the nodes was calculated based on the actual positions of the twelve selected rooms. All the detailed information is summarized in Table 3.  
Based on the number of robots and their capacities, it was assumed that two robots were employed to provide delivery services with three storage compartments. Although the number of robots and their capacities can vary depending on the robot type and given indoor environments, we set these values following previous studies [12; 31; 32]. Additionally, the average speed of the robot was 1 m/s, considering the average walking speed of people indoors [33; 34]. The applied maximum acceleration, maximum deceleration, and safe speed were set to 0.3 m/s\({}^{2}\), 0.6 m/s\({}^{2}\), and 0.5 m/s, respectively [35]. Moreover, the indoor delivery robots are acknowledged to possess sufficient battery power for longer than several hours when fully charged [36]. In regard to the time related to the elevator, both the time spent (s) at a stop and the time spent (s\({}^{\prime}\)) when an intermediate stop occurs were set to 14 s in accordance with past related research [37]. Detailed informa  
Figure 7: Illustrative example building: (**a**) indoor network; (**b**) indoor layout of the first floor. tion on all system parameters, including the above parameters, is provided in Table 4. Note that all the parameters can be flexibly adjusted when the indoor environments change, and these parameters will become more reliable if historical data are available. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of stories & 6 \\ \hline Number of customers & 12 \\ \hline Indoor width & 120 m \\ \hline Indoor depth & 150 m \\ \hline Length between floors (meters) & 5 m \\ \hline Number of robots & 2 \\ \hline \(Q\) & 3 \\ \hline TD & 20 \\ \hline \(V_{max}\) & 1 m/s \\ \hline \(V_{safe}\) & 0.5 m/s \\ \hline \(A\) & 0.3 m/s\({}^{2}\) \\ \hline \(D\) & 0.6 m/s\({}^{2}\) \\ \hline \(w_{peak}\) & 60 s \\ \hline \(w_{normal}\) & 40 s \\ \hline \(w_{off-peak}\) & 20 s \\ \hline \(p_{peak}\) & 0.4 \\ \hline \(p_{normal}\) & 0.3 \\ \hline \(p_{off-peak}\) & 0.1 \\ \hline \(s\) & 14 s \\ \hline \(s^{\prime}\) & 14 s \\ \hline \(V_{e}\) & 1 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: System parameters of the numerical experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Floor** & **Customer ID** & **Delivery Demand** \\ \hline  & 1 & 2 \\ \cline{2-3}
1 & 2 & 2 \\ \hline  & 3 & 1 \\ \cline{2-3}
2 & 4 & 1 \\ \hline  & 5 & 2 \\ \cline{2-3}
3 & 6 & 2 \\ \cline{2-3}  & 7 & 2 \\ \hline  & 8 & 2 \\ \cline{2-3}
4 & 9 & 2 \\ \cline{2-3}
5 & 10 & 1 \\ \cline{2-3}
6 & 12 & 2 \\ \hline  & Sum & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Customer data in the building. Based on the parameters above, the travel time matrix among the nodes must be generated by applying the proposed travel time calculator. This matrix was derived by considering the characteristics of robot movement (e.g., acceleration, deceleration, and cornering) and the additional time required for traveling on the elevator (e.g., elevator waiting time, stops, and occurrence probability of intermediate stops) with the equations presented in Section 3.1.