Polyhedral results and a branch-and-cut algorithm for the double traveling Salesman problem with multiple stacks

In the double TSP with multiple stacks, one performs a Hamiltonian circuit to pick up nn items, storing them in a vehicle with ss stacks of finite capacity qq satisfying last-in-first-out constraints, and then delivers every item by performing a Hamiltonian circuit. We introduce an integer linear programming formulation with arc and precedence variables. We show that the underlying polytope shares some polyhedral properties with the ATSP polytope, which let us characterize large number of facets of our polytope. We convert these theoretical results into a branch-and-cut algorithm for the double TSP with two stacks. Our algorithm outperforms the existing exact methods and solves instances that were previously unsolved.