[Paper Review] Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing

Yiding Feng, Rad Niazadeh+1 more|arXiv (Cornell University)|Oct 21, 2022

Transportation and Mobility Innovations4 citations

TL;DR

This paper introduces a two-stage stochastic matching and pricing framework for ride-hailing platforms to improve supply efficiency and market efficiency by batching demand requests and leveraging future demand uncertainty. It proposes competitive online algorithms—achieving a 3/4 competitive ratio for unweighted matching and 1/2 for joint matching and pricing—using randomized primal-dual methods and prophet inequality techniques, validated on DiDi’s Chengdu dataset with high performance ratios near optimal.

ABSTRACT

Matching and pricing are two critical levers in two-sided marketplaces to connect demand and supply. The platform can produce more efficient matching and pricing decisions by batching the demand requests. We initiate the study of the two-stage stochastic matching problem, with or without pricing, to enable the platform to make improved decisions in a batch with an eye toward the imminent future demand requests. This problem is motivated in part by applications in online marketplaces such as ride hailing platforms. We design online competitive algorithms for vertex-weighted (or unweighted) two-stage stochastic matching for maximizing supply efficiency, and two-stage joint matching and pricing for maximizing market efficiency. In the former problem, using a randomized primal-dual algorithm applied to a family of ``balancing'' convex programs, we obtain the optimal $3/4$ competitive ratio against the optimum offline benchmark. Using a factor revealing program and connections to submodular optimization, we improve this ratio against the optimum online benchmark to $(1-1/e+1/e^2)\approx 0.767$ for the unweighted and $0.761$ for the weighted case. In the latter problem, we design optimal $1/2$-competitive joint pricing and matching algorithm by borrowing ideas from the ex-ante prophet inequality literature. We also show an improved $(1-1/e)$-competitive algorithm for the special case of demand efficiency objective using the correlation gap of submodular functions. Finally, we complement our theoretical study by using DiDi's ride-sharing dataset for Chengdu city and numerically evaluating the performance of our proposed algorithms in practical instances of this problem.

Motivation & Objective

• To model and solve the two-stage stochastic matching problem in two-sided marketplaces where future demand is uncertain but partially known.
• To extend the framework to include joint matching and dynamic pricing decisions to maximize market efficiency.
• To design competitive online algorithms that outperform existing heuristics using theoretical guarantees.
• To evaluate the proposed algorithms on real-world ride-hailing data from DiDi’s Chengdu dataset.
• To provide a theoretical foundation for batching strategies in dynamic matching platforms with future demand information.

Proposed method

• Uses a randomized primal-dual algorithm on a family of 'balancing' convex programs to achieve a 3/4 competitive ratio for unweighted two-stage stochastic matching.
• Applies factor-revealing programs and submodular optimization techniques to improve the competitive ratio to approximately 0.767 (unweighted) and 0.761 (vertex-weighted) against the optimum online benchmark.
• Designs a 1/2-competitive joint matching and pricing algorithm by adapting ex-ante prophet inequality techniques.
• Develops a (1−1/e)-competitive algorithm for the special case of demand efficiency using the correlation gap of submodular functions.
• Employs Monte Carlo simulations on DiDi’s real-world ride-sharing dataset to evaluate performance against offline and online benchmarks.
• Proposes heuristic extensions for multi-stage settings based on single-lookahead application of the two-stage algorithms.

Experimental results

Research questions

• RQ1 What is the optimal competitive ratio achievable for two-stage stochastic matching with unweighted and vertex-weighted supplies?
• RQ2 Can joint matching and pricing decisions improve market efficiency in two-stage stochastic settings, and what competitive ratio can be achieved?
• RQ3 How does the use of distributional knowledge about future demand affect the performance of matching algorithms in practice?
• RQ4 What is the theoretical performance gap between the optimum offline and online benchmarks in two-stage stochastic matching?
• RQ5 Can the two-stage algorithms be extended to multi-stage settings with practical heuristic performance?

Key findings

• The proposed randomized primal-dual algorithm achieves a 3/4 competitive ratio for unweighted two-stage stochastic matching against the optimum offline benchmark.
• By leveraging submodular optimization and factor-revealing programs, the competitive ratio improves to approximately 0.767 for unweighted and 0.761 for weighted cases against the optimum online benchmark.
• A joint matching and pricing algorithm achieves a 1/2 competitive ratio using insights from ex-ante prophet inequalities.
• For the special case of demand efficiency, a (1−1/e)-competitive algorithm is designed using the correlation gap of submodular functions.
• Numerical evaluation on DiDi’s Chengdu dataset shows that proposed policies (SM, SM-Limit, HG) achieve average performance ratios of 0.994–0.998 against the optimum offline, significantly outperforming WBU and GR.
• The performance gap between WBU and GR is 2% on average in the unweighted case and 0.3% in the weighted case, with GR showing less concentration in performance ratios.