A novel extension of the classical vehicle routing and scheduling problems is introduced that integrates aspects of machine scheduling into vehicle routing. Associated with each customer order is a release date that defines the earliest time that the order is available to leave the depot for delivery and a due date that indicates the time by which the order should ideally be delivered to the customer. The objective is to minimize a convex combination of the operational costs and customer service level, represented by the total distance traveled and the total weighted tardiness of delivery, respectively. A path-relinking algorithm (PRA) is proposed to address the problem, and a variety of benchmark instances are generated to evaluate its performance. The PRA exploits the efficiency and aggressive improvement of neighborhood search but relies on a new path-relinking procedure and advanced population management strategies to navigate the search space effectively. To provide a comparator algorithm to the PRA, we embed the neighborhood search into a standard iterated local search algorithm (ILS). Extensive computational experiments on the benchmark instances show that the newly defined features have a significant and varied impact on the problem, and the performance of the PRA dominates that of the ILS algorithm.