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

• Published in: Networks Vol. 55; no. 1; pp. 46 - 59
• Main Authors: Cordeau, Jean-François, Iori, Manuel, Laporte, Gilbert, Salazar González, Juan José
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2010; Wiley
• Subjects: Applied sciences; branch-and-cut; Combinatorics; Combinatorics. Ordered structures; Computer science; control theory; systems; Exact sciences and technology; Graph theory; Information retrieval. Graph; LIFO; Logistics; Mathematics; Operational research and scientific management; Operational research. Management science; pickup and delivery; Sciences and techniques of general use; Theoretical computing; traveling salesman problem; pickup and delivery; traveling salesman problem; Hamiltonian cycle; LIFO system; branch-and-cut; LIFO; Shortest path; Travelling salesman problem; Graph theory; Branch and cut method; Reverse logistics; NP complete problem; Localization; Read head
• ISSN: 0028-3045; 1097-0037; 1097-0037
• DOI: 10.1002/net.20312

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 article 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 min, whereas the largest instance solved contains 25 requests. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010