Tactical Design of Same-Day Delivery Systems

We study tactical models for the design of same-day delivery (SDD) systems. Same-day fulfillment in e-commerce has seen substantial growth in recent years, and the underlying management of such services is complex. Although the literature includes operational models to study SDD, they tend to be detailed, complex, and computationally difficult to solve, and thus may not provide any insight into tactical SDD design variables and their impact on the average performance of the system. We propose a simplified vehicle-dispatching model that captures the “average” behavior of an SDD system from a single stocking location by utilizing continuous approximation techniques. We analyze the structure of optimal vehicle-dispatching policies given our model for two important instance families—the single-vehicle case and the case in which the delivery fleet is large—and develop techniques to find these policies that require only simple computations. We also leverage these results to analyze the case of a finite fleet, proposing a heuristic policy with a worst-case approximation guarantee. We then demonstrate with several example problem settings how this model and these policies can help answer various tactical design questions, including how to select a fleet size, determine an order cutoff time, and combine SDD and overnight order delivery operations. We validate model predictions empirically against a detailed operational model in a computational case study using geographic and Census data for the northeastern metro Atlanta region, and we demonstrate that our model predicts the average number of orders served and dispatch time to within 1%.