A new formulation for the Traveling Deliveryman Problem

• Autores: Méndez-Díaz, I.; Zabala, P.; Lucena, A.
• Año de publicación: 2008
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Appl Math 2008;156(17):3223-3237
• Materia: Branch-and-cut algorithms; Integer programming; Traveling deliveryman problem; Dynamic programming; Hamiltonians; Integer programming; Linearization; Meats; Particle size analysis; Branch-and-Bound; Branch-and-cut algorithms; Computational results; Convex hulls; Cutting plane algorithms; Enumeration trees; Feasible solutions; Hamiltonian path problems; Hamiltonian paths; Integer programming formulations; Linear programming relaxations; Minimum costs; Traveling deliveryman problem; Valid inequalities; Linear programming
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

The Traveling Deliveryman Problem is a generalization of the Minimum Cost Hamiltonian Path Problem where the starting vertex of the path, i.e. a depot vertex, is fixed in advance and the cost associated with a Hamiltonian path equals the sum of the costs for the layers of paths (along the Hamiltonian path) going from the depot vertex to each of the remaining vertices. In this paper, we propose a new Integer Programming formulation for the problem and computationally evaluate the strength of its Linear Programming relaxation. Computational results are also presented for a cutting plane algorithm that uses a number of valid inequalities associated with the proposed formulation. Some of these inequalities are shown to be facet defining for the convex hull of feasible solutions to that formulation. These inequalities proved very effective when used to reinforce Linear Programming relaxation bounds, at the nodes of a Branch and Bound enumeration tree. © 2008 Elsevier B.V. All rights reserved.
Fil:Méndez-Díaz, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Zabala, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.