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An Exact Column Generation Approach to the Capacitated Facility Location Problem

  • Conference paper
Book cover Distribution Logistics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 544))

Abstract

The Capacitated Facility Location Problem (CFLP) is a well-known combinatorial optimization problem with applications in distribution and production planning. It consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs. A variety of lower bounds based on Lagrangean relaxation and subgradient optimization has been proposed for this problem. However, in order to solve large or difficult problem instances information about a primal (fractional) solution is important. Therefore, we employ column generation in order to solve a corresponding master problem exactly. The algorithm uses different strategies for stabilizing the column generation process. Furthermore, the column generation method is employed within a branch-and-price procedure for computing optimal solutions to the CFLP. Computational results are reported for a set of larger and difficult problem instances. The results are compared with computational results obtained from a branch-and-bound procedure based on Lagrangean relaxation and subgradient optimization and a branch-and-bound method that uses the LP relaxation and polyhedral cuts

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Author information

Authors and Affiliations

  1. University of St. Gallen and Institute for Operations Research, University of Zurich, Switzerland

    Andreas Klose

  2. Faculty of Economics and Social Sciences, University of Wuppertal, Germany

    Simon Görtz

Authors
  1. Andreas Klose
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  2. Simon Görtz
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Editor information

Editors and Affiliations

  1. Department of Production and Logistics, University of Augsburg, Universitätsstraße 16, 86159, Augsburg, Germany

    Bernhard Fleischmann

  2. University of St. Gallen, Bodanstraße 6, 9000, St.Gallen, Switzerland

    Andreas Klose

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Klose, A., Görtz, S. (2005). An Exact Column Generation Approach to the Capacitated Facility Location Problem. In: Fleischmann, B., Klose, A. (eds) Distribution Logistics. Lecture Notes in Economics and Mathematical Systems, vol 544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17020-1_1

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