A new formulation for the Traveling Deliveryman Problem

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 Hamiltonia...

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Detalles Bibliográficos
Autores: Méndez-Díaz, I., Zabala, P., Lucena, A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_0166218X_v156_n17_p3223_MendezDiaz
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0166218X_v156_n17_p3223_MendezDiaz
Access Level:acceso abierto
Palabra clave:Branch-and-cut algorithms
Integer programming
Traveling deliveryman problem
Dynamic programming
Hamiltonians
Linearization
Meats
Particle size analysis
Branch-and-Bound
Computational results
Convex hulls
Cutting plane algorithms
Enumeration trees
Feasible solutions
Hamiltonian path problems
Hamiltonian paths
Integer programming formulations
Linear programming relaxations
Minimum costs
Valid inequalities
Linear programming
Descripción
Sumario: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.