On-demand delivery has become increasingly popular around the world. Brick-and-mortar grocery stores, restaurants, and pharmacies are providing fast delivery services to satisfy the growing home delivery demand. Motivated by a large meal and grocery delivery company, we model and solve a multiperiod driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The operator of this system needs to dispatch a set of drivers and specify their delivery routes in a stochastic environment, in which random demand arrives over a fixed number of periods. The resulting dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel approximation framework to approximate the value function via a simplified dispatching program. We then develop efficient exact algorithms for this problem based on Benders decomposition and column generation. We validate the superior performance of our framework and algorithms via extensive numerical experiments. Tested on a real-world data set, we quantify the value of adaptive dispatching and routing in on-time delivery and highlight the need of coordinating these two decisions in a dynamic setting. We show that dispatching multiple vehicles with short trips is preferable for on-time delivery, as opposed to sending a few vehicles with long travel times.
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