A branch-and-cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading

In the Traveling Salesman Problem with Pickup and Delivery (TSPPD) a single vehicle must serve a set of customer requests, each defined by an origin location where a load must be picked up, and a destination location where the load must be delivered. The problem consists of determining a shortest Hamiltonian cycle through all locations while ensuring that the pickup of each request is performed before the corresponding delivery. This paper addresses a variant of the TSPPD in which pickups and deliveries must be performed according to a Last-In First-Out (LIFO) policy. We propose three mathematical formulations for this problem and several families of valid inequalities which are used within a branch-and-cut algorithm. Computational results performed on test instances from the literature show that most instances with up to 17 requests can be solved in less than 10 minutes, while the largest instance solved contains 25 requests.