This paper studies a same-day crowd-sourced delivery setting where in-store customers deliver online orders on their way home. This environment is dynamic and uncertain, characterized by fluctuating numbers of in-store customers and online orders throughout the day, and unpredictable customer decisions to accept or reject delivery tasks. To address these challenges, we develop a two-stage event-driven dynamic matching framework. The first stage leverages short-term predictions about future arrivals of in-store customers and online orders, allowing us to postpone matching decisions for certain drivers and orders, thus optimizing immediate outcomes to maximize order satisfaction over a future time interval. In response to these initial outcomes, the second stage computes the probability of in-store customers accepting matched orders and introduces two compensation models. These models are designed to tailor compensation for each customer, aiming to minimize expected delivery costs at the current decision-making point. Experimental results demonstrate that our framework reduces delivery costs by approximately 15% compared to baseline methods, highlighting its potential to improve the efficiency of crowd-sourced delivery systems in a constantly changing market.@en

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%.@en

Crowd-Sourced Delivery Services (CDS) use in-store customers, as crowd-shippers, to deliver online orders directly to other customers. As independent contractors, the crowd-shippers are free to decide whether to accept or reject the online orders assigned by the retailer. High order rejection rates can significantly influence the retailer’s delivery costs due to frequent reassignments and shifting the orders to more expensive professional fleet. To incentivize crowd-shippers to accept the matched orders, in this work, we propose a two-stage optimization framework that integrates bipartite matching with an individual compensation scheme. The first stage of the optimization framework computes the optimal matching between crowd-shippers and online orders to minimize the delivery detours and unassigned orders. Given the matching solutions as inputs, the second stage computes personal compensation for each crowd-shipper based on the characteristic of the matched order and his or her acceptance behavior uncertainty, with the goal of minimizing the expected total delivery cost of the retailer. Numerical experiments are conducted using the survey data to illustrate the performance of the proposed framework and compare it with existing matching and pricing strategies in the literature. Our results show that the proposed framework reduces the delivery cost by up to more than 15% and reduces the crowd-shippers’ rejection rate by an average of 55%.@en