Solving the Asymmetric Travelling Salesman Problem with time windows by branch-and-cut

Many optimization problems have several equivalent mathematical models. It is often not apparents which of these models is most suitable for practical computation, in particular, when a certain application with a specific ran ge of instance sizes is in focus. Our paper addresses the Asymmetric Travel ling Salesman Problem with time windows (ATSP-TW) from such a point of view . The real-world application we aim at is die control of a stacker crane in a warehouse. We have implemented codes based on three alternative integer programming fo rmulations of the ATSP-TW and more than ten heuristies. Computational resul ts for real-world instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two model s we considered - at least for our special application - and that the heuri stics provide acceptable solutions.