A Branch-and-Cut Algorithm for the Double Traveling Salesman Problem with Multiple Stacks

Authors:
Manuel A. Alba Martínez;Jean-François Cordeau;Mauro Dell'Amico;Manuel Iori
Affiliations:
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy;Canada Research Chair in Logistics and Transportation and CIRRELT, HEC Montréal, Montréal, Québec H3T 2A7, Canada;Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy;Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy
Venue:
INFORMS Journal on Computing
Year:
2013

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Abstract

The double traveling salesman problem with multiple stacks is a variant of the pickup and delivery traveling salesman problem in which all pickups must be completed before any delivery. In addition, items can be loaded on multiple stacks in the vehicle, and each stack must obey the last-in-first-out policy. The problem consists of finding the shortest Hamiltonian cycles covering all pickup and delivery locations while ensuring the feasibility of the loading plan. We formulate the problem as two traveling salesman problems linked by infeasible path constraints. We also introduce several strengthenings of these constraints, which are used within a branch-and-cut algorithm. Computational results performed on instances from the literature show that the algorithm outperforms existing exact algorithms. Instances with up to 28 requests 58 nodes have been solved to optimality.