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Parcel delivery cost minimization with time window constraints using trucks and drones

We propose a model for solving a parcel delivery problem with a fleet of trucks embedded with drones. When appropriate, drones are loaded with a parcel, launched directly from the truck, and sent to a client. Afterward, the drones autonomously return to the truck to be replenished and recharged. Inspired by the case of a large European logistics provider, the proposed modeling framework confronts realistic delivery problems involving time windows, limited drone autonomy, and the eligibility of clients to be served by drones. The considered global cost function includes fixed daily vehicle fares, driver wages, and the fuel and electricity consumption to power trucks and drones. To solve the problems at hand, we propose a mixed‐integer linear programming formulation and an adaptive large neighborhood search. Moreover, we introduce an efficient modeling framework to manage the numerous synchronization constraints induced by the simultaneous use of trucks and drones. We analyze the benefits of this new transportation concept for delivery problems involving up to 100 parcels. Results show that truck‐and‐drone solutions can reduce costs up to 34% compared to traditional truck‐only delivery. From a managerial perspective, we show that a certain percentage of client locations must be reachable by drone to make truck‐and‐drone solutions competitive (i.e., if the fixed costs of the drones are compensated for by the savings on truck routes) and compare the cost structures of truck‐and‐drone versus truck‐only solutions.