## 1 Introduction
On the one hand, passengers' privacy is better maintained since they share their rides not with strangers, but with parcels, which could be particularly attractive to those who value their privacy during shared rides. Additionally, passengers might experience less detour time compared to ride-pooling with other passengers, given that parcels can endure extended detour routes, so passengers can be given priority for pick-up or drop-off, while being pooled with the parcels. In order to realize last-mile delivery in the transit co-modal system through ride-pooling services that pool passengers and parcels into the same service vehicles, a critical issue is the proper planning of parcel locker locations, which aligns with the problem of \"freight hub location design\" for integrated passenger-parcel transportation. These parcel lockers (or hubs) provide temporary storage for parcels following transit transportation and before their collection by ride-sourcing vehicles. The planning objective may be flexible, depending on whom (passengers or parcels) we aim to serve primarily. Despitethe previous studies on the freight hub location problem in co-modal systems, we rarely see any research conducted in the context of leveraging ride-pooling services to perform last-mile delivery (see Section 2 for a review of the related literature). Therefore, it remains unclear how to optimally plan parcel locker locations for the transit co-modal systems with ride-pooling last-mile delivery and what the key factors are that affect the planning results. To fill the research gaps, this paper proposes a data-driven optimization framework for determining the optimal parcel locker locations in a transit co-modal market, in which last-mile delivery is provided by integrating parcels transportation with ride-sourcing passengers. While there are multiple use cases of parcel lockers (e.g., business-to-consumer and consumer-to-consumer parcel lockers), we focus on the location optimization of parcel lockers that provide temporary storage for parcels. The location optimization problem is formulated as a \(p\)-median model. We use the trip data extracted from a Shenzhen taxi trip dataset and the location data of candidate parcel lockers as inputs to the proposed \(p\)-median model to perform city-wide optimization. To strike a balance between computational efficiency and solution quality, the proposed optimization framework applies a random sampling method to the considered data. Random samples are generated, each containing a subset of trips of the whole trip dataset. The \(p\)-median model is then solved for each sample, and the optimal locations of the parcel lockers are finally determined based on each candidate location's frequency of being selected among all the samples. Numerical experiments are conducted to examine the effectiveness of the proposed optimization framework and explore the effects of crucial model parameters on the optimization outcome. Furthermore, we propose a ranking-based classification for the candidate locations based on the experiment results, through which policy implications are provided. The contributions of this paper are summarized as follows. * We develop an optimization framework based on random sampling to determine the optimal parcel locker locations in a transit co-modal system incorporating ride-pooling services to perform last-mile delivery;
* We propose a ranking-based classification for the candidate parcel locker locations, classifying the candidate locations into five types and offering policy implications;
* We discover that the average minimum detour distance of ride-pooling passengers can be positively affected by the density of ride-pooling demand and negatively impacted by the number of selected locations, thereby providing insights into the planning of parcel locker locations. The remainder of the paper is organized as follows. Section 2 reviews the existing literature related to this study.