The Uncapacitated Asymmetric Traveling Salesman Problem with Multiple Stacks

Abstract

Abstract. In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then we deliver every item by performing a hamiltonian circuit. 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 this linear relaxation.

New formulation and branch‐and‐cut algorithm for the pickup and delivery traveling salesman problem with multiple stacks

“…Borne et al. () addressed the uncapacitated version of DTSPMS. They provided a polyhedral study of the problem and an integer linear programming (ILP) formulation for the case where two stacks are available and for which the linear programming relaxation is polynomial time solvable.…”

“…The method is based on finding the k-best tours to each of the separate pickup and delivery routes and matching the solutions leading to a feasible loading plan. Borne et al (2012) addressed the uncapacitated version of DTSPMS. They provided a polyhedral study of the problem and an integer linear programming (ILP) formulation for the case where two stacks are available and for which the linear programming relaxation is polynomial time solvable.…”