The Ride-Pool Matching Problem (RMP) is central to on-demand ride-pooling services, where vehicles must be matched with multiple requests while adhering to service constraints such as pickup delays, detour limits, and vehicle capacity. Most existing RMP solutions assume passengers are picked up and dropped off at their original locations, neglecting the potential for passengers to walk to nearby spots to meet vehicles. This assumption restricts the optimization potential in ride-pooling operations. In this paper, we propose a novel matching method that incorporates extended pickup and drop-off areas for passengers. We first design a tree-based approach to efficiently generate feasible matches between passengers and vehicles. Next, we optimize vehicle routes to cover all designated pickup and drop-off locations while minimizing total travel distance. Finally, we employ dynamic assignment strategies to achieve optimal matching outcomes. Experiments on city-scale taxi datasets demonstrate that our method improves the number of served requests by up to 13\% and average travel distance by up to 21\% compared to leading existing solutions, underscoring the potential of leveraging passenger mobility to significantly enhance ride-pooling service efficiency.

The popularity of on-demand ride pooling is owing to the benefits offered to customers (lower prices), taxi drivers (higher revenue), environment (lower carbon footprint due to fewer vehicles) and aggregation companies like Uber (higher revenue). To achieve these benefits, two key interlinked challenges have to be solved effectively: (a) pricing -- setting prices to customer requests for taxis; and (b) matching -- assignment of customers (that accepted the prices) to taxis/cars. Traditionally, both these challenges have been studied individually and using myopic approaches (considering only current requests), without considering the impact of current matching on addressing future requests. In this paper, we develop a novel framework that handles the pricing and matching problems together, while also considering the future impact of the pricing and matching decisions. In our experimental results on a real-world taxi dataset, we demonstrate that our framework can significantly improve revenue (up to 17% and on average 6.4%) in a sustainable manner by reducing the number of vehicles (up to 14% and on average 10.6%) required to obtain a given fixed revenue and the overall distance travelled by vehicles (up to 11.1% and on average 3.7%). That is to say, we are able to provide an ideal win-win scenario for all stakeholders (customers, drivers, aggregator, environment) involved by obtaining higher revenue for customers, drivers, aggregator (ride pooling company) while being good for the environment (due to fewer number of vehicles on the road and lesser fuel consumed).

State-of-the-art order dispatching algorithms for ridesharing batch passenger requests and allocate them to a fleet of vehicles in a centralized manner, optimizing over the estimated values of each passenger-vehicle matching using integer linear programming (ILP). Using good estimates of future values, such ILP-based approaches are able to significantly increase the service rates (percentage of requests served) for a fixed fleet of vehicles. However, such approaches that focus solely on maximizing efficiency can lead to disparities for both drivers (e.g., income inequality) and passengers (e.g., inequality of service for different groups). Existing approaches that consider fairness only do it for naive assignment policies, require extensive training, or look at only single-sided fairness. We propose a simple incentive-based fairness scheme that can be implemented online as a part of this ILP formulation that allows us to improve fairness over a variety of fairness metrics. Deriving from a lens of variance minimization, we describe how these fairness incentives can be formulated for two distinct use cases for passenger groups and driver fairness. We show that under mild conditions, our approach can guarantee an improvement in the chosen metric for the worst-off individual. We also show empirically that our Simple Incentives approach significantly outperforms prior art, despite requiring no retraining; indeed, it often leads to a large improvement over the state-of-the-art fairness-aware approach in both overall service rate and fairness.

Real-time ridesharing systems such as UberPool, Lyft Line, GrabShare have become hugely popular as they reduce the costs for customers, improve per trip revenue for drivers and reduce traffic on the roads by grouping customers with similar itineraries. The key challenge in these systems is to group the "right" requests to travel together in the "right" available vehicles in real-time, so that the objective (e.g., requests served, revenue or delay) is optimized. This challenge has been addressed in existing work by: (i) generating as many relevant feasible (with respect to the available delay for customers) combinations of requests as possible in real-time; and then (ii) optimizing assignment of the feasible request combinations to vehicles. Since the number of request combinations increases exponentially with the increase in vehicle capacity and number of requests, unfortunately, such approaches have to employ ad hoc heuristics to identify a subset of request combinations for assignment. Our key contribution is in developing approaches that employ zone (abstraction of individual locations) paths instead of request combinations. Zone paths allow for generation of significantly more "relevant" combinations (in comparison to ad hoc heuristics) in real-time than competing approaches due to two reasons: (i) Each zone path can typically represent multiple request combinations; (ii) Zone paths are generated using a combination of offline and online methods. Specifically, we contribute both myopic (ridesharing assignment focussed on current requests only) and non-myopic (ridesharing assignment considers impact on expected future requests) approaches that employ zone paths. In our experimental results, we demonstrate that our myopic approach outperforms (with respect to both objective and runtime) the current best myopic approach for ridesharing on both real-world and synthetic datasets.

Markov Decision Processes (MDPs) are an effective model to represent decision processes in the presence of transitional uncertainty and reward tradeoffs. However, due to the difficulty in exactly specifying the transition and reward functions in MDPs, researchers have proposed uncertain MDP models and robustness objectives in solving those models. Most approaches for computing robust policies have focused on the computation of maximin policies which maximize the value in the worst case amongst all realisations of uncertainty. Given the overly conservative nature of maximin policies, recent work has proposed minimax regret as an ideal alternative to the maximin objective for robust optimization. However, existing algorithms for handling minimax regret are restricted to models with uncertainty over rewards only and they are also limited in their scalability. Therefore, we provide a general model of uncertain MDPs that considers uncertainty over both transition and reward functions. Furthermore, we also consider dependence of the uncertainty across different states and decision epochs. We also provide a mixed integer linear program formulation for minimizing regret given a set of samples of the transition and reward functions in the uncertain MDP. In addition, we provide two myopic variants of regret, namely Cumulative Expected Myopic Regret (CEMR) and One Step Regret (OSR) that can be optimized in a scalable manner. Specifically, we provide dynamic programming and policy iteration based algorithms to optimize CEMR and OSR respectively. Finally, to demonstrate the effectiveness of our approaches, we provide comparisons on two benchmark problems from literature. We observe that optimizing the myopic variants of regret, OSR and CEMR are better than directly optimizing the regret.