Matching Drivers to Riders: A Two-stage Robust Approach

Abstract

Matching demand (riders) to supply (drivers) efficiently is a fundamental problem for ridesharing 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 by an average of 30% in our experimental results.

Two-stage Matching and Pricing with Applications to Ride Hailing

“…In their model, a batch of new edges arrive adversarially in the second stage, and their algorithm first finds a maximum fractional matching using the matching skeleton and then removes some of the edges in the first stage through a randomized procedure to obtain a 2 3 -competitive ratio. Another work that is conceptually related to our two-stage matching problem is the recent work of Housni et al (2020), which is inspired by the idea of robust multi-stage optimization (e.g., Bertsimas et al 2010Bertsimas et al , 2011.…”

Online Bipartite Matching with Advice: Tight Robustness-Consistency Tradeoffs for the Two-Stage Model

“…In this paper we focus on the two-stage online matching model of Feng et al (2021), introducing advice to this model and fully characterizing the tradeoff between obeying vs. disobeying the advice. We note that a multi-stage online matching model motivated by batching has also been recently considered in Feng and Niazadeh (2020), and two-stage matching has been formulated as a robust optimization problem in Housni et al (2020).…”

Batching and Optimal Multi-stage Bipartite Allocations

“…For two-stage stochastic matching, various models with different objectives have been studied in Kong and Schaefer (2006); Escoffier et al (2010);Katriel et al (2008) and more recently in Feng et al (2020b). Another work that is conceptually related to us is the recent work of Housni et al (2020), which is inspired by the idea of robust multi-stage optimization (e.g., Bertsimas et al, 2010Bertsimas et al, , 2011. They consider a two-stage robust optimization for cost-minimization of the matching, where future demand uncertainty is modeled using a set of demand scenarios (specified explicitly or implicitly).…”