Reinforced stable matching for Crowd-Sourced Delivery Systems under stochastic driver acceptance behavior

Crowd-Sourced Delivery Systems (CDS) depend on occasional drivers to deliver parcels directly to online customers. These freelance drivers have the flexibility to accept or reject orders from the platform, leading to a stochastic and often unstable matching process for delivery assignments. This instability results in frequent rematching, delayed deliveries, decreased customer satisfaction, and increased operational costs, all highlighting the critical need for improved matching stability within CDS. While traditional stable matching theory provides a foundation, it primarily addresses static and deterministic scenarios, making it less effective in the dynamic and unpredictable environments typical of CDS. Addressing this gap, this study extends the classic Gale–Shapley (GS) stable matching algorithm by incorporating tailored compensations for drivers, incentivizing them to accept assigned orders and thus improving the stability of matchings, even with the inherent uncertainties of driver acceptance. We prove that the proposed mechanism can generate reinforced stable matching results based on tailored compensation values. Also, our numerical study shows that this reinforced stable matching approach significantly outperforms traditional methods in terms of both matching stability and cost-effectiveness. It reduces the order rejection rate to as low as 1% and cuts operational costs by up to 18%.