## 7 Conclusions  
This paper proposes an optimization framework for the planning of parcel locker locations in a transit co-modal system that leverages the on-demand ride-pooling services for last-mile delivery. The parcels are assumed to be transported via the transit system, stored in the selected parcel lockers, and then delivered to their final destinations by sharing a fleet of on-demand ride-pooling vehicles with passengers. To prioritize passenger convenience while enabling efficient passenger-parcel pooling, the routing sequence for a combined passenger-parcel ride is designed to follow the order of passenger origin, parcel origin, passenger destination, and parcel destination. A \(p\)-median model that minimizes the average passenger detour time is developed to solve the optimal locations of parcel lockers and optimal matching between the passengers and the parcel lockers. The taxi trip data and the candidate location data for parcel lockers in Shenzhen, China, are used as inputs to the \(p\)-median model. In view of the scale of the dataset, an optimization framework based on random sampling is then developed to determine the optimal parcel locker locations according to each candidate's frequency of being selected in the sample. We conducted numerical experiments to evaluate the effectiveness of the proposed optimization framework, explore its properties, and perform sensitivity analyses on the key model parameters. The results demonstrate that the optimal parcel locker locations selected by the proposed optimization framework align with up to 70% of the locations chosen by the samples, and the percentage keeps growing as more trips are included in the samples. Moreover, we discover that the candidate parcel locker locations can be classified into five types according to the changes in their rankings of being selected, namely (1) stable, (2) rising, (3) falling, (4) concave, and (5) convex. While the reasons for the emergence of the five candidate types may be complicated, we suggest some policy implications for the planners to carefully identify candidate types and determine the number of selected locations properly. Last, but not least, the results of sensitivity analyses reveal that the average passenger detour distance is positively related to the density of passenger demand and is negatively impacted by the number of selected locations. Moreover, we also identify the minimum distance between any pair of selected locations as an important factor in location planning, as it may significantly affect the candidates' rankings. Our proposed optimization framework and the implications derived from the numerical experiments are expected to be used by service providers who wish to integrate ride-pooling service with the transit co-modal systems to plan parcel locker locations. We acknowledge that this paper has several limitations, which can be addressed through future studies. For example, we only consider the trip demand in one hour due to data availability, which may lead to biased optimization results because of the variability in trip demand at different times of the day and on weekdays and weekends. More robust results can be expected from future studies that include data from other time periods. In addition, the pure random sampling method adopted in the optimization framework may also lead to biased optimization results. Other sampling techniques, such as those that account for the spatial and temporal distributions of the trip demand, can be further applied to generate the samples for the optimization framework. Last, but not least, our model only considers integrating ride-pooling passengers with single parcels, while the case of multiple parcels warrants further investigation. Follow-up studies can be conducted by extending the PM model to account for multiple parcels. Conceptualization, Z.L. and B.L. ; methodology, Z.L. and B.L. ; software, Z.L. ; validation, Z.L. ; formal analysis, Z.L. and B.L. ; investigation, Z.L. ; resources, B.L. ; data curation, Z.L. ; writing--original draft preparation, Z.L.