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Matching Drivers to Riders: A Two-Stage Robust Approach

Authors Omar El Housni, Vineet Goyal, Oussama Hanguir, Clifford Stein

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Author Details

Omar El Housni
  • School of Operations Research and Information Engineering, Cornell Tech, New York, NY, USA
Vineet Goyal
  • Industrial Engineering and Operations Research, Columbia University, New York, NY, USA
Oussama Hanguir
  • Industrial Engineering and Operations Research, Columbia University, New York, NY, USA
Clifford Stein
  • Industrial Engineering and Operations Research, Columbia University, New York, NY, USA

Funding

  • Stein, Clifford: Research partly supported by NSF Grants CCF-1714818 and CCF-1822809.

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Omar El Housni, Vineet Goyal, Oussama Hanguir, and Clifford Stein. Matching Drivers to Riders: A Two-Stage Robust Approach. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.12

Abstract

Matching demand (riders) to supply (drivers) efficiently is a fundamental problem for ride-hailing 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 this two-stage robust matching is NP-hard under both explicit and implicit models of uncertainty. We present constant approximation algorithms for both models of uncertainty under different settings and show they improve significantly over standard greedy approaches.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • matching
  • robust optimization
  • approximation algorithms

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