Branch-and-cut for the pickup and delivery traveling salesman problem with FIFO loading

This paper introduces a branch-and-cut algorithm for a variant of the pickup and delivery traveling salesman problem in which pickups and deliveries must obey the first-in-first-out policy. We propose a new mathematical formulation of the problem and several families of valid inequalities which are used within the branch-and-cut algorithm. Computational experiments on instances from the literature show that this algorithm outperforms existing exact algorithms, and that some instances with up to 25 requests (50 nodes) can be solved in reasonable computing time.