Matching demand with supply in crowdsourcing 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. For the special case with homogeneous and independent acceptance responses, an exact mixed-integer linear program and LP formulations are achievable, 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 a convex relaxation of the original problem that admits a mixed-integer exponential cone program (MIECP) formulation. We analyze the structural properties of this approximation and establish its parametric performance guarantees. We also characterize conditions under which it can dominate a deterministic approximation. 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, which makes it particularly promising for large-scale matching problems.

翻译：众包物流平台上的需求与供应匹配必须应对工人参与的不确定性。受这一挑战的启发，我们研究了随机供应商拒绝情形下的两阶段“推荐匹配”问题，其中每个需求在最终匹配决策前被初步推荐给多个潜在供应商。我们构建了一个明确捕捉供应商不确定接受行为的随机优化模型。在响应同质且独立的特殊情形中，可得到精确的混合整数线性规划与线性规划公式，但一般问题无法实现高效建模。特别地，我们的分析表明，确定性线性近似方法在此类设置中可能表现极差。为克服这一局限，我们提出一种基于原始问题凸松弛的新近似方法，该方法可构建为混合整数指数锥规划（MIECP）模型。我们分析了该近似的结构性质并建立了其参数性能保证，同时刻画了其能够优于确定性近似的条件。基于合成数据与真实货运数据的大量实验验证了我们方法的有效性。与基准方法相比，基于MIECP的解在匹配性能接近最优的同时，计算时间减少超过90%，使其尤其适用于大规模匹配问题。