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Cutting Stock Problems

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Book cover Column Generation

Abstract

Column generation has been proposed by Gilmore and Gomory to solve cutting stock problem, independently of Dantzig-Wolfe decomposition. We survey the basic models proposed for cutting stock and the corresponding solution approaches. Extended Dantzig-Wolfe decomposition is surveyed and applied to these models in order to show the links to Gilmore-Gomory model. Branching schemes discussion is based on the subproblem formulation corresponding to each model. Integer solutions are obtained by combining heuristics and branch-and-price schemes. Linear relaxations are solved by column generation. Stabilization techniques such as dual-optimal inequalities and stabilized column generation algorithms that have been proposed to improve the efficiency of this process are briefly discussed.

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Author information

Authors and Affiliations

  1. École Polytechnique and GERAD, Canada

    Hatem Ben Amor

  2. Universidade do Minho, Portugal

    José Valério de Carvalho

Authors
  1. Hatem Ben Amor
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  2. José Valério de Carvalho
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Editor information

Editors and Affiliations

  1. GERAD and École Polytechnique de Montréal, Canada

    Guy Desaulniers

  2. GERAD and HEC Montréal, Canada

    Jacques Desrosiers

  3. GERAD and Northeastern University, Boston

    Marius M. Solomon

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© 2005 Springer Science+Business Media, Inc.

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Ben Amor, H., Valério de Carvalho, J. (2005). Cutting Stock Problems. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds) Column Generation. Springer, Boston, MA. https://doi.org/10.1007/0-387-25486-2_5

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