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A Probabilistic Approach for Demand-Aware Ride-Sharing Optimization

Qiulin Lin, Wenjie Xu, Minghua Chen, Xiaojun Lin

TL;DR

The paper addresses joint demand-aware ride-sharing optimization under probabilistic future demand, introducing a probabilistic framework that assigns requests to vehicles in a stochastic manner. It reformulates the problem into tractable linear-combinatorial forms and leverages a dual-subgradient algorithm to achieve a $(1-1/e)$-approximation for the original NP-hard objective. By employing a time-expanded graph and a concave surrogate, the approach yields scalable solutions with provable guarantees, demonstrated on real Manhattan traces where demand-aware joint routing outperforms demand-oblivious baselines by up to 46% in pickups. The work provides a practical baseline for fleet-level optimization in modern ride-sharing platforms and suggests extensions to multi-rider settings and long-term performance optimization.

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.

A Probabilistic Approach for Demand-Aware Ride-Sharing Optimization

TL;DR

The paper addresses joint demand-aware ride-sharing optimization under probabilistic future demand, introducing a probabilistic framework that assigns requests to vehicles in a stochastic manner. It reformulates the problem into tractable linear-combinatorial forms and leverages a dual-subgradient algorithm to achieve a -approximation for the original NP-hard objective. By employing a time-expanded graph and a concave surrogate, the approach yields scalable solutions with provable guarantees, demonstrated on real Manhattan traces where demand-aware joint routing outperforms demand-oblivious baselines by up to 46% in pickups. The work provides a practical baseline for fleet-level optimization in modern ride-sharing platforms and suggests extensions to multi-rider settings and long-term performance optimization.

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 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.

Paper Structure

This paper contains 30 sections, 6 theorems, 27 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Settings
  3. Transportation Network and Region Graph
  4. Travel Request
  5. Vehicle State
  6. Request-Vehicle Assignment and Routing
  7. Problem Formulation
  8. Ride-Sharing Feasibility
  9. Feasibility of Request-Vehicle Assignments
  10. Problem Formulation
  11. A Dual-Subgradient Algorithm
  12. Reformulation over a Time-Expanded Graph
  13. A $\left(1-1/e\right)$ Approximation
  14. A Linear-Combinatorial Reformulation
  15. Dual Sub-Gradient Decent Algorithm
  16. ...and 15 more sections

Key Result

Proposition 2

The request-vehicle assignment probability vectors $\left[\boldsymbol{y}_{i},1\leq i\leq N\right]$ are feasible if and only if they satisfy that, for all $1\leq i\leq N$, $1\leq k\leq K$, $t\in\mathcal{T}$, and $v,u\in\mathcal{V}$, Let $\mathcal{Y}$ be the set of all feasible request-vehicle assignment vectors.

Figures (7)

  • Figure 1: An example of the transportation network and the corresponding region graph. Each region has a representative node marked as a red triangle. The constructed region graph is shown in Fig. \ref{['fig:R-network.example']}. Each node in the region graph represents a region. Each edge $(u,v)$ in the region graph represents a fastest path in the transportation network from the representative node of region $u$ to that of region $v$. For example, the edge in color red in the region graph in Fig. \ref{['fig:R-network.example']} represents the path in color red in the transportation network in Fig. \ref{['fig:T-network.example']}.
  • Figure 2: In this particular instance where 3 requests appear in a region of 5 vehicles, the 3 requests are assigned to vehicle 2, 4, and 5.
  • Figure 3: Probability heatmaps calculated by using \ref{['equ:PrempCal']} for the time slot $t=216$, corresponding to the time window $\left[18:00, 18:05\right]$ of the day. As seen, the distributions are highly heterogeneous across regions and many regions have limited demands. As such, it is important to perform a demand-aware, instead of demand-oblivious, design and to jointly assign requests to vehicles, in order to achieve proper demand-supply balancing and avoid passenger pickup conflict.
  • Figure 4: The empirical pickups under the setting of delay factor $\alpha=1.3$ and fleet size $N=50$.
  • Figure 5: Empirical pickups for $\alpha=1.3$ and the time slot $t_s=204$, corresponding to the time window $\left[17:00, 17:05\right]$ of the day.
  • ...and 2 more figures

Theorems & Definitions (8)

  • Definition 1
  • Proposition 2
  • Proposition 3
  • Definition 4
  • Proposition 5
  • Theorem 6
  • Corollary 7
  • Theorem 8