arXiv:2507.01749v1 Announce Type: new Abstract: This paper examines the use of in-store customers as delivery couriers in a centralized crowd-shipping system, targeting the growing need for efficient last-mile delivery in urban areas. We consider a brick-and-mortar retail setting where shoppers are offered compensation to deliver time-sensitive online orders. To manage this process, we propose a Markov Decision Process (MDP) model that captures key uncertainties, including the stochastic arrival of orders and crowd-shippers, and the probabilistic acceptance of delivery offers. Our solution approach integrates Neural Approximate Dynamic Programming (NeurADP) for adaptive order-to-shopper assignment with a Deep Double Q-Network (DDQN) for dynamic pricing. This joint optimization strategy enables multi-drop routing and accounts for offer acceptance uncertainty, aligning more closely with real-world operations. Experimental results demonstrate that the integrated NeurADP + DDQN policy achieves notable improvements in delivery cost efficiency, with up to 6.7\% savings over NeurADP with fixed pricing and approximately 18\% over myopic baselines. We also show that allowing flexible delivery delays and enabling multi-destination routing further reduces operational costs by 8\% and 17\%, respectively. These findings underscore the advantages of dynamic, forward-looking policies in crowd-shipping systems and offer practical guidance for urban logistics operators.