Robust Drone Delivery with Weather Information

Problem definition: Drone delivery has recently garnered significant attention due to its potential for faster delivery at a lower cost than other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations, leading to late deliveries. Methodology/results: To mitigate the risk of delivery delays caused by wind uncertainty, we propose a two-period drone scheduling model to robustly optimize the delivery schedule. In this framework, the scheduling decisions are made in the morning, with the provision for different delivery schedules in the afternoon that adapt to updated weather information available by midday. Our approach minimizes the essential riskiness index, which can simultaneously account for the probability of tardy delivery and the magnitude of lateness. Using wind observation data, we characterize the uncertain flight times via a cluster-wise ambiguity set, which has the benefit of tractability while avoiding overfitting the empirical distribution. A branch-and-cut (B&C) algorithm is developed for this adaptive distributionally framework to improve its scalability. Our adaptive distributionally robust model can effectively reduce lateness in out-of-sample tests compared with other classical models. The proposed B&C algorithm can solve instances to optimality within a shorter time frame than a general modeling toolbox. Managerial implications: Decision makers can use the adaptive robust model together with the cluster-wise ambiguity set to effectively reduce service lateness at customers for drone delivery systems. Funding: This work was supported by the National Natural Science Foundation of China Grants 72101049 and 72232001, the Natural Science Foundation of Liaoning Province Grant 2023-BS-091, the Fundamental Research Funds for the Central Universities Grant DUT23RC(3)045, and the Major Project of the National Social Science Foundation Grant 22&ZD151. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2022.0339 .