Approximate dynamic programming for pickup and delivery problem with crowd-shipping

We study a variant of dynamic pickup and delivery crowd-shipping operation for delivering online orders within a few hours from a brick-and-mortar store. This crowd-shipping operation is subject to a high degree of uncertainty due to the stochastic arrival of online orders and crowd-shippers that impose several challenges for efficient matching of orders to crowd-shippers. We formulate the problem as a Markov decision process and develop an Approximate Dynamic Programming (ADP) policy using value function approximation for obtaining a highly scalable and real-time matching strategy while considering temporal and spatial uncertainty in arrivals of online orders and crowd-shippers. We incorporate several algorithmic enhancements to the ADP algorithm, which significantly improve the convergence. We compare the ADP policy with an optimization-based myopic policy using various performance measures. Our numerical analysis with varying parameter settings shows that ADP policies can lead to up to 25.2% cost savings and a 9.8% increase in the number of served orders. Overall, we find that our proposed framework can guide crowd-shipping platforms for efficient real-time matching decisions and enhance the platform delivery capacity.