Abstract
The one-dimensional cutting stock problem (CSP) is as follows: Given an unlimited number of pieces of identical stock material of length L the task is to cut b i pieces of length ℓ i for i ∈ I = {1, …, m} while minimizing the number of stock material pieces needed. Let ℓ = (ℓ1, …, ℓ m )T and b = (b 1, …, b m )T. Without loss of generality, let L ≥ ℓ1 > … > ℓ m > 0 and b i > 0 for i ∈ I
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References
P. C. Gilmore and R. E. Gomory. A linear programming approach to the cutting-stock problem (Part I). Oper. Res., 9:849–859, 1961.
E.A. Mukhacheva, G.N. Belov, V.M. Kartak, and A.S. Mukhacheva. Linear one-dimensional cutting-packing problems: … Technical report, Aviation Univ. Ufa, 1999.
G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, New York, 1988.
G. Scheithauer and J. Terno. A branch-and-bound algorithm for solving one-dimensional cutting stock problems exactly. Applicationes Mathematicae, 23.2:151–167, 1995.
G. Scheithauer, J. Terno, A. Müller and G. Belcv. Solving one-dimensional cutting stock problems exactly with a cutting plane algorithm. Technical Report MATH-NM-06-1999, Dresden University of Technology, 1999.
P. Schwerin and G. Wäscher. A new lower bound for the bin-packing problem and its integration into MTP. Techn. Report 98/26, MLU Halle-Wittenberg, 1998.
G. Wäscher and T. Gau. Heuristics for the one-dimensional cutting stock problem: A computational study. OR Spektrum, 18:131–144, 1996.
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© 2000 Springer-Verlag Berlin Heidelberg
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Scheithauer, G. (2000). Solving One-Dimensional Cutting Stock Problems Exactly with a Cutting Plane Algorithm. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds) Operations Research Proceedings 1999. Operations Research Proceedings 1999, vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58300-1_16
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DOI: https://doi.org/10.1007/978-3-642-58300-1_16
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