A Probabilistic Approach for Demand-Aware Ride-Sharing Optimization

TL;DR

This paper introduces a probabilistic demand-aware framework for ride-sharing that optimizes request-vehicle assignment to maximize pickups, demonstrating significant improvements over demand-oblivious methods through scalable heuristics.

Contribution

It proposes a novel probabilistic approach with a scalable heuristic for joint request-vehicle assignment, providing performance guarantees in a complex NP-hard optimization problem.

Findings

Up to 46% increase in passenger pickups compared to demand-oblivious schemes.

Joint fleet-level optimization yields 19% more pickups than individual vehicle optimization.

The heuristic achieves a (1-1/e) approximation under certain conditions.

Abstract

Ride-sharing is a modern urban-mobility paradigm with tremendous potential in reducing congestion and pollution. Demand-aware design is a promising avenue for addressing a critical challenge in ride-sharing systems, namely joint optimization of request-vehicle assignment and routing for a fleet of vehicles. In this paper, we develop a probabilistic demand-aware framework to tackle the challenge. We focus on maximizing the expected number of passenger pickups, given the probability distributions of future demands. The key idea of our approach is to assign requests to vehicles in a probabilistic manner. It differentiates our work from existing ones and allows us to explore a richer design space to tackle the request-vehicle assignment puzzle with a performance guarantee but still keeping the final solution practically implementable. The optimization problem is non-convex, combinatorial, and NP-hard in nature. As a key contribution, we explore the problem structure and propose an elegant approximation of the objective function to develop a dual-subgradient heuristic. We characterize a condition under which the heuristic generates a $\left(1-1/e\right)$ approximation solution. Our solution is simple and scalable, amendable for practical implementation. Results of numerical experiments based on real-world traces in Manhattan show that, as compared to a conventional demand-oblivious scheme, our demand-aware solution improves the passenger pickups by up to 46%. The results also show that joint optimization at the fleet level leads to 19% more pickups than that by separate optimizations at individual vehicles.