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This paper presents a new approach for formulating the delivery problem bydrones with general energy consumption models where the drones visit a set ofplaces to deliver parcels to customers. Drones can perform multiple trips thatstart and end at a central depot while visiting several customers along theirpaths. The problem determines the routing and scheduling decisions of thedrones in order to minimize the total transportation cost of serving customers.For the first time, the new formulation approach enables us to use the bestavailable energy consumption model without the need of any extraapproximations. Though the approach works in a very general setting includingnon-convex energy consumption models, it is also computationally efficient asthe resulting optimization model has a linear relaxation. A numerical study on255 benchmark instances with up to 50 customers and a specific energy functionindicate that all the instances can be solved 20 times faster on average usingthe new formulation when compared to the best existing branch-and-cutalgorithm. All the 15 benchmark instances with 50 customers are solved exactly,whereas none of them has been solved optimally before. Moreover, new instanceswith up to 150 customers are solved with small error bounds within a few hours.The new approach can be simply applied to consider the extra energy requiredwhen a drone needs to continue hovering until opening the delivery time window.It can also be applied to the case where the flight time is dependent on thedrone's payload weight. Owing to the flexibility of the new approach, thesechallenging extensions are formulated as linear optimization models for thefirst time.

Delivery by Drones with Arbitrary Energy Consumption Models: A New Formulation Approach