Data-driven robust optimization for a multi-trip truck-drone routing problem

Using drones along with conventional vehicles, such as trucks, can potentially improve the cost-effectiveness and speed of delivery operations. This research considers a multi-trip truck-drone routing problem under uncertainty. Each truck is allowed to take multiple trips from the depot, while each drone is allowed to perform a single trip from the launch locations. Based on customer preferences, deliveries are grouped into deliveries by trucks to distribution centers and deliveries by drones from distribution centers to customers. A mixed-integer linear programming model is formulated to minimize the sum of the waiting times of all customers. To deal with uncertainty, a new two-stage clustering algorithm that uses multiple-kernel learning-based and single-kernel learning-based methods is introduced to construct uncertainty sets. In the case of column-wised uncertainty, a two-stage clustering with a dimensional separation algorithm is developed to avoid over-conservatism. A two-step solution method is provided for solving the proposed robust model to reduce the CPU time. The performance of the proposed algorithms is evaluated on several test problems. The results indicate that the developed algorithms can effectively avoid over-conservatism, reduce variables and constraints of the data-driven robust counterpart model, and reduce the CPU time required to solve the problem.