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.

翻译：众包物流平台中的供需匹配必须应对工作者参与的不确定性。针对这一挑战，我们研究了随机供应商拒绝下的两阶段“推荐匹配”问题，其中每个需求在最终匹配决策前会先被推荐给多个潜在供应商。我们构建了一个显式刻画供应商不确定接受行为的随机优化模型。研究表明，在供应商接受响应具有同质性和独立性的特殊情况下，可获得精确的混合整数线性规划模型，但该通用问题不存在高效建模形式。特别地，我们的分析表明确定性线性近似方法在此类场景中可能产生任意差的性能。为克服这一局限，我们提出了一种基于混合整数指数锥规划的新型近似方法，并建立了其参数化性能保证。在合成数据与真实货运数据上的大量实验验证了本方法的有效性。相较于基准方法，我们基于MIECP的解决方案在实现近乎最优匹配性能的同时，将计算时间降低了90%以上。