In the capacitated routing-scheduling problem (CRSP) for a multimodal delivery system, the first leg is performed by a truck that makes a tour starting from the depot, visiting some facilities from a set of candidate robot stations. The second and last leg of the delivery is performed by Autonomous Delivery Robots (ADRs), starting from the facilities and ending at the customer’s doorstep. The demand that can be served at each robot station is limited. Each customer has a scheduled delivery time and must be served from a single station. If the robot arrives after this time, the difference between the time of the delivery and the scheduled time is counted as the tardiness for the customer. The CRSP asks to select a tour for the truck and a feasible assignment of customers to facilities such that the total tardiness of delivery is minimized. Existing literature tackles an uncapacitated version of this problem which is modeled with a compact formulation and solved by Benders decomposition. We propose an extended formulation and branch-and-price approach to solve the capacitated problem, which is shown to outperform a direct solving of the (adapted) compact formulation. We also perform a sensitivity analysis on key parameters such as the number and capacities of robot stations in the network and the tightness of delivery deadlines, to derive managerial insights.