Del poliedro del agente viajero gráfico al de rutas de vehículos con demanda compartida

Questiio: Quaderns d'Estadistica, Sistemes, Informatica i Investigació Operativa, ISSN 0210-8054, Vol. 24, Nº. 3, 2000, pags. 495-528
Source: OAI

ABSTRACT En este trabajo abordamos el estudio del poliedro asociado al Problema de Rutas de Vehículos con Demanda Compartida, problema de distribución que surge cuando hay que repartir mercancías a un conjunto de clientes utilizando una flota fija de vehículos de capacidad limitada. El objetivo es diseñar las rutas de forma que se minimice la distancia total recorrida. Se diferencia de otros problemas más conocidos de rutas con capacidades en que se permite abastecer la demanda de cada cliente utilizando más de un vehículo. Presentamos resultados poliédricos que se obtienen como extensión de otros previamente conocidos para el Problema del Agente Viajero Gráfico

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    ABSTRACT: An algorithm is described for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a "polyhedral" cutting-plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph. The cuts are generated by several identification procedures that have been described in a companion paper. Whenever the cutting-plane procedure does not terminate with an optimal solution the algorithm uses a tree- search strategy that, as opposed to branch-and-bound, keeps on producing cuts after branching. The algorithm has been implemented in FORTRAN. Two different linear programming (LP) packages have been used as the LP solver. The implementation of the algorithm and the interface with one of the LP solvers is described in sufficient detail to permit the replication of our experiments. Computational results are reported with up to 42 STSPs with sizes ranging from 48 to 2,392 nodes. Most of the medium-sized test problems are taken from the literature; all others are large-scale real-world problems. All of the instances considered in this study were solved to optimality by the algorithm in "reasonable" computation times.
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