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The Uncapacitated Asymmetric Traveling Salesman Problem with Multiple Stacks

  • Sylvie Borne
  • Roland Grappe
  • Mathieu Lacroix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

Abstract

In the uncapacitated asymmetric traveling salesman problem with multiple stacks, one first performs a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then delivers every item by performing a second hamiltonian circuit. Here, we are interested in the convex hull of the arc-incidence vectors of such couples of hamiltonian circuits.

For the general case, we determine the dimension of this polytope, and show that every facet of the asymmetric traveling salesman polytope defines one of its facets. For the special case with two stacks, we provide an integer linear programming formulation whose linear relaxation is polynomial-time solvable, and we propose new families of valid inequalities to reinforce the latter.

Keywords

asymmetric traveling salesman problem stacks polytope facets formulation valid inequalities 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sylvie Borne
    • 1
  • Roland Grappe
    • 1
  • Mathieu Lacroix
    • 1
  1. 1.Laboratoire d’Informatique de Paris-Nord, UMR CNRS 7030Université ParisVilletaneuseFrance

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