Data-Driven Matching for Impatient and Heterogeneous Demand and Supply

• 成果类型: Article; Early Access
• 署名作者: Liu, Weiliang; Ward, Amy R.; Zhang, Xun
• 署名单位: City University of Hong Kong; University of Chicago; Southern University of Science & Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.1115
• 发表日期: 2026-06-04
• 关键词: bipartite matching; unknown parameters; Statistical learning; finite-sample bound; impatience; reneging; abandonment fluid model; discrete-review policy; e-asymptotic optimality; empirical measures; policies; CONVERGENCE

摘要

This paper develops a framework that integrates finite-sample statistical learning with queueing asymptotic analysis to design matching policies. The stochastic matching model we consider assumes heterogeneous demand (customers) and heterogeneous supply (workers) arrive randomly over time, each with a randomly sampled patience time, and are lost (renege) if forced to wait longer than that time to be matched. Because the interarrival and patience-time distributions are unknown, matching decisions must be made based on historical (offline) data. We leverage asymptotic analysis to formulate a deterministic, data-driven (fluid) matching problem (DDMP) that approximates the original stochastic matching problem. We establish finite-sample statistical guarantees on the objective value gap between the DDMP solution and the ground-truth matching problem solution, which requires a novel uniform error bound involving the patience-time quantile function. We show that a discrete-review, estimate-then-match-type policy is epsilon-asymptotically optimal with high probability as arrival rates grow large.