Formulations and algorithms for the Pickup and Delivery Traveling Salesman Problem with Multiple Stacks.

•We introduce new Integer Linear Programming formulations for the Pickup and Delivery Traveling Salesman Problem with Multiple Stacks.•We propose valid inequalities for the formulations along with separation procedures for each of them.•We implement Branch & Cut algorithms for the proposed formulations.•Computational results show that the developed algorithms outperforms the other exact algorithms in the literature.•We obtained new proven optimal solutions for several benchmark instances.