Energy-constrained multi-visit TSP with multiple drones considering non-customer rendezvous locations

• We study a multi-visit traveling salesman problem with multiple drones. • Drone energy consumption in all phases of flight is considered to plan drone trips. • We propose a subproblem to locate candidate non-customer retrieval nodes for drones. • MILP formulations are developed for the proposed subproblem and problem. • Effective heuristic and matheuristic solution approaches are provided for problems. This paper introduces the energy-constrained multi-visit traveling salesman problem with multiple drones considering non-customer rendezvous locations (EM-TSPDs). A ground vehicle equipped with multiple drones that can serve multiple customers per trip performs deliveries. Before solving the EM-TSPDs, the non-customer rendezvous location subproblem (NRLP) is addressed to locate candidate non-customer rendezvous nodes so that all drone customers can be covered by drones. The importance of this full coverage is that all drone customers can reap the benefits of drone delivery by receiving fast delivery or being served in areas that are inaccessible by road network. We propose MILP formulations for the NRLP and EM-TSPDs that can be solved with standard MILP solvers. Due to the NP-hard nature of the problem, heuristic algorithms are provided to solve medium and large-scale instances in a time-efficient manner. Numerical results show that using multiple drones that can serve multiple customers per trip leads to a reduction in the makespan. Taking into account the battery energy consumption at different phases of the drone flight leads to more accurate and realistic modeling of the drone endurance. In addition, the impact of adding non-customer rendezvous locations is investigated.