The Robotaxi Placement Problem: Minimizing Expected ETA for Stochastic Demand

TL;DR

This paper formalizes the robotaxi placement problem to minimize expected rider wait times, providing theoretical bounds, algorithms, and empirical results demonstrating practical effectiveness.

Contribution

It introduces a stochastic optimization framework for robotaxi placement, with approximation algorithms, inapproximability bounds, and a polynomial-time algorithm for tree metrics.

Findings

Sampling robotaxi locations yields a 2-approximation.

Inapproximability bounds are established via a novel reduction.

Variance-reduced random placement performs well in real-world data.

Abstract

Autonomous ride-hailing platforms must strategically position idle robotaxis to minimize the wait times of prospective riders. We formalize this as the \emph{robotaxi placement problem} ($k$-RP). Given a finite metric space and a demand distribution over its points, the goal is to position $k$ robotaxis to minimize the expected total distance in a perfect matching between the robotaxis and $k$ random riders. We present several theoretical results for this stochastic optimization problem. First, we observe that sampling robotaxi locations independently according to the demand distribution yields a randomized $2$-approximation algorithm. Second, we present an explicit inapproximability bound via a novel gap-preserving reduction from the maximum coverage problem. Furthermore, while it is not even clear whether the exact expected cost of a placement can be computed efficiently on general metrics, we design an exact polynomial-time dynamic programming algorithm for $k$-RP in tree metrics by decoupling the stochastic matching dependencies. Finally, empirical evaluations on real-world ride-hailing data reveal that a variance-reduced random placement strategy is highly effective in practice, yielding expected wait times that are very close to those obtained by computationally heavy exact algorithms for the uniform capacitated $k$-median problem.