An Enhanced Approximate Dynamic Programming Approach to On-demand Ride Pooling

Ride-pooling services have been growing in popularity, increasing the need for efficient and effective operations. The main goal of ride-pooling services is to maximize the number of passengers served while minimizing wait and delay times. However, factors such as the timing and volume of passenger requests, pick-up and drop-off locations, available vehicle capacity, and the trajectory to fulfill multiple requests introduce high degrees of uncertainty, creating challenges for ride-pooling operators. This study aims to expand the current state-of-the-art Approximate Dynamic Programming (ADP) approach for ride-pooling services, introduce key extensions, and perform a comparative analysis with the Neural Approximate Dynamic Programming (NeurADP) approach to optimize the efficiency and effectiveness of these services. Specifically, we develop an ADP approach that incorporates three important problem specifications: (i) pick-up and drop-off deadlines, (ii) vehicle rebalancing, and (iii) allowing more than two passengers in a vehicle. We conduct a detailed numerical study with the New York City taxi-cab dataset and a novel dataset of taxi-cab requests collected in the city of Chicago. We also provide a sensitivity analysis on key model parameters such as wait and delay times, passenger group sizes, and vehicle capacity, along with the investigation of the effects of vehicle rebalancing. Our comparative analysis highlights the strengths and limitations of both ADP and NeurADP methodologies. Network density and road directionality are found to significantly impact the performance. NeurADP is found to be more efficient in learning value function approximations for larger and more complex problem settings than the ADP approach. However, for smaller settings, ADP is shown to outperform NeurADP.