Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment

  • Authors:
  • Ivan Contreras;Juan A. Díaz;Elena Fernández

  • Affiliations:
  • Departament d' Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain;Departamento Ingeniería Industrial y Mecánica, Universidad de las Américas, 72820 Puebla, México;Departament d' Estadística i Investigació Operativa, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

  • Venue:
  • INFORMS Journal on Computing
  • Year:
  • 2011

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Abstract

This paper presents a branch-and-price algorithm for the capacitated hub location problem with single assignment, in which Lagrangean relaxation is used to obtain tight lower bounds of the restricted master problem. A lower bound that is valid at any stage of the column generation algorithm is proposed. The process to obtain this valid lower bound is combined with a constrained stabilization method that results in a considerable improvement on the overall efficiency of the solution algorithm. Numerical results on a battery of benchmark instances of up to 200 nodes are reported. These seem to be the largest instances that have been solved to optimality for this problem.