Recommend-to-Match with Random Supply Rejections: Formulation, Approximation, and Analysis

Matching demand with supply in crowd-sourcing logistics platforms must contend with uncertain worker participation. Motivated by this challenge, we study a two-stage ``recommend-to-match" problem under stochastic supplier rejections, where each demand is initially recommended to multiple potential suppliers prior to final matching decisions. We formulate a stochastic optimization model that explicitly captures uncertain supplier acceptance behavior. We show that an exact mixed-integer linear formulation is obtainable for the special case with homogeneous and independent acceptance responses, but the general problem does not admit an efficient formulation. Particularly, our analysis reveals that deterministic linear approximation methods can perform arbitrarily poorly in such settings. To overcome this limitation, we propose a new approximation approach based on mixed-integer exponential cone programming (MIECP) and establish its parametric performance guarantees. Extensive experiments on synthetic data and real-world freight data validate the effectiveness of our approach. Our MIECP-based solution achieves near-optimal matching performance while reducing computation time by over 90% compared to benchmark methods.