Vehicle routing problem with en-route delivery

Traditional last-mile delivery usually requires customers to offer predetermined locations for receiving parcels. However, the advancement of information and communication technology enables the collection and utilization of real-time information for more innovative, flexible, and cost-saving ways of delivery. This paper introduces a new last-mile delivery problem where en-route deliveries can occur at any node or arc along customers' trajectories. Customers' trajectories are first converted into candidate time windows across nodes and arcs, with exactly one time window per customer required to enable delivery. This problem formulates a general routing problem that minimizes total travel cost, which is then transformed into a node-routing problem solvable through mixed-integer linear programming. Results show that flexible en-route deliveries significantly reduce transportation costs compared to traditional delivery approaches where delivery can be made at only one location. Moreover, en-route delivery is particularly effective when service time at arcs is shorter than at nodes.