A Variable Neighborhood Descent Matheuristic for the Drone Routing Problem with Beehives Sharing

In contemporary urban logistics, drones will become a preferred transportation mode for last-mile deliveries, as they have shown commercial potential and triple-bottom-line performance. Drones, in fact, address many challenges related to congestion and emissions and can streamline the last leg of the supply chain, while maintaining economic performance. Despite the common conviction that drones will reshape the future of deliveries, numerous hurdles prevent practical implementation of this futuristic vision. The sharing economy, referred to as a collaborative business model that foster sharing, exchanging and renting resources, could lead to operational improvements and enhance the cost control ability and the flexibility of companies using drones. For instance, the Amazon patent for drone beehives, which are fulfilment centers where drones can be restocked before flying out again for another delivery, could be established as a shared delivery systems where different freight carriers jointly deliver goods to customers. Only a few studies have addressed the problem of operating such facilities providing services to retail companies. In this paper, we formulate the problem as a deterministic location-routing model and derive its robust counterpart under the travel time uncertainty. To tackle the computational complexity of the model caused by the non-linear energy consumption rates in drone battery, we propose a tailored matheuristic combining variable neighborhood descent with a cut generation approach. The computational experiments show the efficiency of the solution approach especially compared to the Gurobi solver.