Local delivery networks expect drivers to make deliveries to and/or pickups from customers using the shortest routes in order to minimize costs, delivery time, and environmental impact. However, in real-world applications, it is often the case that not all customers are known when planning the initial delivery route. Instead, additional customers become known while the driver is making deliveries or pickups. Before serving the new demand requests, the vehicle will return to the depot for restocking. In other words, there exists a precedence relation in the delivery route to visit the depot before delivering new orders. The uncertainty in new customer locations can lead to expensive rerouting of the tour, as drivers revisit previous neighborhoods to serve the new customers. We address this issue by constructing the delivery route with the knowledge that additional customers will appear, using historical demand patterns to guide our predictions for the uncertainty. We model this network delivery problem as a precedence-constrained asymmetric traveling salesman problem using mixed-integer optimization. Experimental results show that the proposed robust optimization approach provides an effective delivery route under the uncertainty of customer demands. KEYWORDS demand uncertainty, dynamic vehicle routing, precedence-constrained traveling salesman problem, robust optimization, same-day delivery network Networks. 2019;73:434-452.wileyonlinelibrary.com/journal/net FIGURE 1 (A) Ill-placed route planning under uncertainty-the tour will back-track to a previously visited neighborhood to reach the newly emerged nodes; (B) well-placed route planning under uncertainty-the tour does not need to return to previously visited neighborhoods to reach the newly emerged nodes. Note that the white unshaded circles are the known nodes, on which the original TSP is calculated. At a particular time, the tour reaches w * , uncertainty is realized, and the new, shaded nodes are added to the problem. The tour will return to the depot, d, before visiting the new nodes