## 3 Scenario Design for the Ride-Pooling Services with Passenger-Parcel Integration  
We give a necessary introduction to the scenario design of the ride-pooling services with passenger-parcel integration before we dive into the detailed formulation of the parcel locker location planning problem. In the existing literature, ride-pooling services with passenger-parcel integration usually take place between a ride-pooling passenger and no less than one parcel(s). When a passenger is ride-pooled with more than one parcel, he/she may have to spend more time picking up/dropping off the parcels, which may further lower the passengers' willingness to participate in integration and add to model complexity. Therefore, we only consider the case where a passenger and a parcel are pooled into a ride.  
There are various service scenario designs of passenger-parcel integration in ride-pooling services, which can be distinguished according to the pick-up and drop-off sequences of the pooled passengers and parcels. For example, in [37], two ride-pooling service scenarios were classified based on the routing sequence of the service vehicles, which are termed _moderate integration_ and _full integration_. Figure 1a,b provides a simple illustration of these two scenarios. Moderate integration stipulates that the passenger does not deviate from his/her trip path from the origin to the destination due to picking up or dropping off the parcel. This means that although the passenger and the parcel are integrated into the same service vehicle, their trip paths do not overlap. Full integration, however, relaxes the non-overlapping constraint and allows for the service vehicle to detour to pick up or drop off the parcel while the passenger is onboard. That being said, one should be aware that passengers under full integration may experience extra detour time if the vehicle drops off the parcel first, and then the passengers. Therefore, to give priority to passengers so as to sustain their willingness to get involved in such an integrated service mode, we adapt full passenger-parcel integration, but require that the service vehicle routing follows the sequence of passenger origin, parcel origin, passenger destination, and parcel destination (as illustrated in Figure 1b). Such a requirement guarantees that passengers are not fully compromised on parcel delivery in terms of routing and is expected to strike a balance between the costs of passenger travel and parcel delivery.  
The usage and operational model of parcel lockers can also have significant impacts on the functionality of the integrated service. Parcel lockers can be categorized into several types based on their use case. For instance, business-to-consumer parcel lockers are deployed by retailers and e-commerce companies for curbside pick-up or in-store package collection, enhancing customer convenience. Consumer-to-consumer parcel lockers support peer-to-peer exchange in re-commerce or community-based transactions, addressing need for secure, centralized drop-off/pick-up points. In terms of operational models for parcel lockers, two commonly seen models are the open locker and the closed locker systems. An open locker system allows for multiple delivery service providers to use the same locker infrastructure, promoting shared access and reducing redundancy [39]. In contrast, a closed locker system is typically operated by a single logistics provider or retailer, serving only their specific customers [40]. The parcel lockers considered in this study refer to those providing temporary storage to the parcels and are exclusively owned by the integrated service provider.