A multiple-drone arc routing and mothership coordination problem

This paper considers the optimisation problems that arise in coordinating a tandem between a mothership vehicle and a fleet of drones. Each drone can be launched from the mothership to perform a task. After completing their tasks, the drones return to the mothership to recharge their batteries and be ready for a new task. Tasks consist of (partially) visiting graphs of a given length to provide some services or to carry out a surveillance/inspection activity. The goal is to minimise the overall time of travelling carried out by the mothership (makespan) while satisfying some requirements in terms of fractions of visits to the target graphs. In all cases, we develop exact formulations resorting to mixed-integer second-order cone programmes that are compared on a testbed of instances to assess their performance. We also develop a matheuristic algorithm that provides reasonable solutions. Computational experiments show the usefulness of our methodology in different scenarios.