Cutting Stock Problems

Hatem Ben Amor () and José Valério de Carvalho ()
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Hatem Ben Amor: École Polytechnique and GERAD
José Valério de Carvalho: Universidade do Minho

Chapter Chapter 5 in Column Generation, 2005, pp 131-161 from Springer

Abstract: 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.

Keywords: Knapsack Problem; Column Generation; Master Problem; Integer Solution; Linear Programming Relaxation (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (14)

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DOI: 10.1007/0-387-25486-2_5

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