A new MILP formulation for the flying sidekick traveling salesman problem

Nowadays, truck-and-drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem (FS-TSP) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck-and-drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc-based integer linear programming formulation for the FS-TSP. The solution of such formulation required the development of a branch-and-cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state-of-the-art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.