A Nested Decomposition Approach to a Three-Stage, Two-Dimensional Cutting-Stock Problem
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DOI: 10.1287/mnsc.47.6.864.9809
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References listed on IDEAS
- P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
- Robert Weismantel, 1996. "Hilbert Bases and the Facets of Special Knapsack Polytopes," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 886-904, November.
- Valerio de Carvalho, J. M. & Guimaraes Rodrigues, A. J., 1995. "An LP-based approach to a two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 580-589, August.
- Riehme, Jan & Scheithauer, Guntram & Terno, Johannes, 1996. "The solution of two-stage guillotine cutting stock problems having extremely varying order demands," European Journal of Operational Research, Elsevier, vol. 91(3), pages 543-552, June.
- Beasley, J. E., 1985. "An algorithm for the two-dimensional assortment problem," European Journal of Operational Research, Elsevier, vol. 19(2), pages 253-261, February.
- Vanderbeck, F. & Wolsey, L. A., 1996. "An exact algorithm for IP column generation," LIDAM Reprints CORE 1242, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
- David Pisinger, 1999. "Core Problems in Knapsack Algorithms," Operations Research, INFORMS, vol. 47(4), pages 570-575, August.
- P. C. Gilmore & R. E. Gomory, 1965. "Multistage Cutting Stock Problems of Two and More Dimensions," Operations Research, INFORMS, vol. 13(1), pages 94-120, February.
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Cited by:
- Cui, Yaodong & Huang, Baixiong, 2012. "Reducing the number of cuts in generating three-staged cutting patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 358-365.
- Jean-François Côté & Manuel Iori, 2018. "The Meet-in-the-Middle Principle for Cutting and Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 646-661, November.
- Jianyu Long & Zhong Zheng & Xiaoqiang Gao & Panos M. Pardalos & Wanzhe Hu, 2020. "An effective heuristic based on column generation for the two-dimensional three-stage steel plate cutting problem," Annals of Operations Research, Springer, vol. 289(2), pages 291-311, June.
- Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
- Samir Elhedhli & Jean-Louis Goffin, 2005. "Efficient Production-Distribution System Design," Management Science, INFORMS, vol. 51(7), pages 1151-1164, July.
- Cui, Yaodong & Yang, Liu & Zhao, Zhigang & Tang, Tianbing & Yin, Mengxiao, 2013. "Sequential grouping heuristic for the two-dimensional cutting stock problem with pattern reduction," International Journal of Production Economics, Elsevier, vol. 144(2), pages 432-439.
- Silva, Elsa & Alvelos, Filipe & Valério de Carvalho, J.M., 2010. "An integer programming model for two- and three-stage two-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 205(3), pages 699-708, September.
- Yaodong Cui, 2013. "A new dynamic programming procedure for three-staged cutting patterns," Journal of Global Optimization, Springer, vol. 55(2), pages 349-357, February.
- Muter, İbrahim & Sezer, Zeynep, 2018. "Algorithms for the one-dimensional two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 20-32.
- Tilk, Christian & Drexl, Michael & Irnich, Stefan, 2019. "Nested branch-and-price-and-cut for vehicle routing problems with multiple resource interdependencies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 549-565.
- Frank Hennig & Bjørn Nygreen & Marco E. Lübbecke, 2012. "Nested column generation applied to the crude oil tanker routing and scheduling problem with split pickup and split delivery," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 298-310, April.
- François Clautiaux & Ruslan Sadykov & François Vanderbeck & Quentin Viaud, 2019. "Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 265-297, September.
- Alberto Caprara & Andrea Lodi & Michele Monaci, 2005. "Fast Approximation Schemes for Two-Stage, Two-Dimensional Bin Packing," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 150-172, February.
- Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
- Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
- Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
- Fabio Furini & Enrico Malaguti & Dimitri Thomopulos, 2016. "Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 736-751, November.
- Hadj Salem, Khadija & Silva, Elsa & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "Mathematical models for the two-dimensional variable-sized cutting stock problem in the home textile industry," European Journal of Operational Research, Elsevier, vol. 306(2), pages 549-566.
- Carolin Bauerhenne & Jonathan Bard & Rainer Kolisch, 2024. "Robust Routing and Scheduling of Home Healthcare Workers: A Nested Branch-and-Price Approach," Papers 2407.06215, arXiv.org.
- de Gelder, E.R. & Wagelmans, A.P.M., 2007. "The two-dimensional cutting stock problem within the roller blind production process," Econometric Institute Research Papers EI 2007-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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Keywords
Cutting Stock; Trim Loss; Knapsack Problems; Integer Programming; Nested Decomposition;All these keywords.
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