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An Exact Column Generation Approach to the Capacitated Facility Location Problem

In: Distribution Logistics

Author

Listed:
  • Andreas Klose

    (University of Zurich)

  • Simon Görtz

    (University of Wuppertal)

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

Suggested Citation

  • Andreas Klose & Simon Görtz, 2005. "An Exact Column Generation Approach to the Capacitated Facility Location Problem," Lecture Notes in Economics and Mathematical Systems, in: Bernhard Fleischmann & Andreas Klose (ed.), Distribution Logistics, pages 3-26, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-17020-1_1
    DOI: 10.1007/978-3-642-17020-1_1
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