Fleet resupply by drones for last-mile delivery

The Vehicle Routing Problem with Release Dates and Drone Resupply consists of routing a fleet of trucks to deliver orders that arrive at a depot over time. During the delivery horizon, the trucks can return to the depot to collect newly arrived orders, or these orders can be resupplied to the trucks along their routes via drones dispatched from the depot. A Mixed-Integer Linear Programming (MILP) formulation is developed for the version of the problem where order arrival times at the depot (generally termed order release dates) are known beforehand. To address large-size instances, we devise a unified matheuristic approach that provides high-quality solutions for both the truck-and-drone and the truck-only versions of the problem. In this approach, truck routes are iteratively modified using a tabu search scheme, where a subordinate fast MILP model defines optimal loading operations (truck depot returns and drone resupplies) for promising truck routes. We perform extensive numerical experiments with instances of up to 100 customers. Results show the effectiveness of the matheuristic approach for solving both the truck-and-drone and the truck-only versions of the problem. We also show the benefits of drone resupply to reduce completion times and the number of times the trucks need to return to the depot to collect newly released orders. Furthermore, we provide several managerial insights regarding fleet utilization and consolidation.