## 5 An Optimization Framework for Parcel Locker Locations with Randomly Sampled Passenger Trip Data
### The Shenzhen Taxi Trip Data  
This study uses the taxi trip data from Shenzhen, China, as the input for the developed optimization framework. Shenzhen is one of the major cities of China, located on the southern border of the country. According to the local census data [46], the city had a permanent population of approximately 17.68 million and covered an area of 1997 square kilometers at the end of 2023. The high population density, extensive urban mobility, and well-developed infrastructure have laid a solid foundation for the implementation of co-modality in the city. The taxi dataset was recorded on 1 September 2019 (Sunday), capturing 26,698 taxi trips serviced by 13,631 taxis, all within the hour from 18:00:00 to 19:00:00 (We thank Shenzhen Urban Transport Planning Center Co., Ltd. for providing the data.). Due to data availability, we have adopted such a one-hour taxi dataset as a proxy for passengers' demand for ride-pooling services. We acknowledge the importance of having a set of virtual ride-sourcing demand data that covers other time periods of the day (i.e., morning, noon, and night), other days of the week (especially workdays), and some special events and holidays. As such, the optimization framework can further account for demand variations across different time frames, thereby providing more nuanced insights and improving the generalizability of the findings. In the considered dataset, each trip record is assumed to represent an intended passenger for ride-pooling services and includes the following information (see Table 1):  
* The anonymized taxi plate number;
* The start time of the trip;
* The longitude and the latitude (both in GPS coordinates) of the trip origin and destination.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Trip ID**} & \multicolumn{2}{l}{**Taxi Plate**} & \multirow{2}{*}{**Start Time**} & \multirow{2}{*}{**Origin Longitude**} & \multirow{2}{*}{**Origin Latitude**} & **Destination** & **Destination** \\  & **(Anonymized)** & & & & **Longitude** & **Latitude** \\ \hline
1 & ******** & 18:00:00 & 113.881195 & 22.56668 & 113.861404 & 22.603367 \\
2 & **** & 18:00:00 & 113.903885 & 22.516727 & 113.91072 & 22.539614 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
26,698 & **** & 18:59:05 & 114.05342 & 22.5356 & 114.12182 & 22.567995 \\ \hline \hline \end{tabular} Note: **** & \multicolumn{1}{c}{****} & \multicolumn{1}{c}{****} & \multicolumn{1}{c}{****} & \multicolumn{1}{c}{****} \\ \hline \hline \end{tabular}
\end{table}
Table 1: The Shenzhen taxi trip data.  
We then show the spatial distribution of the origins and destinations of all 26,698 trips in Figures 3 and 4, respectively. The figures reveal a clear concentration of taxi trips in the downtown areas of Shenzhen, particularly in the southern part of the city, where trip generation and attraction are significantly higher. In contrast, the rural regions, such as those in the eastern and northwestern parts of the city, exhibit much lower demand. Additionally, the patterns of trip origins and destinations closely mirror each other, indicating the consistent flow of people within these densely populated urban zones.