Matching Drivers to Riders: A Two-stage Robust Approach

TL;DR

This paper introduces a two-stage robust optimization approach for matching drivers to riders in ride-sharing, accounting for demand uncertainty, and demonstrates its effectiveness through approximation algorithms and real-world data testing.

Contribution

It develops a novel two-stage robust optimization framework for ride-matching that considers future demand uncertainty and provides approximation algorithms with proven performance guarantees.

Findings

Algorithms significantly outperform myopic solutions.

Reduction in maximum wait time for riders.

Framework applicable to real-world ride-sharing data.

Abstract

Matching demand (riders) to supply (drivers) efficiently is a fundamental problem for ride-sharing platforms who need to match the riders (almost) as soon as the request arrives with only partial knowledge about future ride requests. A myopic approach that computes an optimal matching for current requests ignoring future uncertainty can be highly sub-optimal. In this paper, we consider a two-stage robust optimization framework for this matching problem where future demand uncertainty is modeled using a set of demand scenarios (specified explicitly or implicitly). The goal is to match the current request to drivers (in the first stage) so that the cost of first-stage matching and the worst-case cost over all scenarios for the second-stage matching is minimized. We show that the two-stage robust matching is NP-hard under various cost functions and present constant approximation algorithms for different settings of our two-stage problem. Furthermore, we test our algorithms on real-life taxi data from the city of Shenzhen and show that they substantially improve upon myopic solutions and reduce the maximum wait time of the second-stage riders.