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Theoretical Paper

An efficient approach for large-scale two-dimensional guillotine cutting stock problems

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Pages 1270-1277 | Received 01 Mar 1997, Accepted 01 Jul 1998, Published online: 20 Dec 2017

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Hao Zhang, Shaowen Yao, Qiang Liu, Lijun Wei, Libin Lin & Jiewu Leng. (2023) An exact approach for the constrained two-dimensional guillotine cutting problem with defects. International Journal of Production Research 61:9, pages 2986-3003.
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Mateus Martin, Reinaldo Morabito & Pedro Munari. (2021) A top-down cutting approach for modeling the constrained two- and three-dimensional guillotine cutting problems. Journal of the Operational Research Society 72:12, pages 2755-2769.
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Yaodong Cui. (2012) Extended block patterns for the two-dimensional cutting stock problem. Engineering Optimization 44:6, pages 657-672.
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E G Birgin, R D Lobato & R Morabito. (2012) Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm. Journal of the Operational Research Society 63:2, pages 183-200.
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M. Kang & K. Yoon. (2011) An improved best-first branch-and-bound algorithm for unconstrained two-dimensional cutting problems. International Journal of Production Research 49:15, pages 4437-4455.
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Y. Cui, T. Gu & W. Hu. (2008) An algorithm for the constrained two-dimensional rectangular multiple identical large object placement problem. Optimization Methods and Software 23:3, pages 375-393.
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Hao Zhang, Shaowen Yao, Qiang Liu, Jiewu Leng & Lijun Wei. (2023) Exact approaches for the unconstrained two-dimensional cutting problem with defects. Computers & Operations Research 160, pages 106407.
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Henrique Becker, Mateus Martin, Olinto Araujo, Luciana S. Buriol & Reinaldo Morabito. (2023) Comparative analysis of mathematical formulations for the two‐dimensional guillotine cutting problem. International Transactions in Operational Research.
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Elsa Silva, José Fernando Oliveira, Tiago Silveira, Leandro Mundim & Maria Antónia Carravilla. (2023) The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems. Omega 114, pages 102738.
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Carlos Diego Rodrigues, Adriana Cristina Cherri & Silvio Alexandre de Araujo. (2023) Strip based compact formulation for two-dimensional guillotine cutting problems. Computers & Operations Research 149, pages 106044.
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Manuel Iori, Vinícius Loti de Lima, Silvano Martello & Michele Monaci. (2021) 2DPackLib: a two-dimensional cutting and packing library. Optimization Letters 16:2, pages 471-480.
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Chengran Xu, Jiepeng Liu, Sheng Li, Zhou Wu & Y. Frank Chen. (2021) Optimal brick layout of masonry walls based on intelligent evolutionary algorithm and building information modeling. Automation in Construction 129, pages 103824.
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Mauro Russo, Maurizio Boccia, Antonio Sforza & Claudio Sterle. (2019) Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization. International Transactions in Operational Research 27:2, pages 794-834.
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István Borgulya. (2018) An EDA for the 2D knapsack problem with guillotine constraint. Central European Journal of Operations Research 27:2, pages 329-356.
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Lijun Wei, Qian Hu, Andrew Lim & Qiang Liu. (2018) A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem. European Journal of Operational Research 270:2, pages 448-474.
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Thiago Alves de Queiroz, Pedro Henrique Del Bianco Hokama, Rafael Crivellari Saliba Schouery & Flávio Keidi Miyazawa. (2017) Two-dimensional Disjunctively Constrained Knapsack Problem: Heuristic and exact approaches. Computers & Industrial Engineering 105, pages 313-328.
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Mauro Russo, Antonio Sforza & Claudio Sterle. 2017. Optimization and Decision Science: Methodologies and Applications. Optimization and Decision Science: Methodologies and Applications 461 472 .
Lijun Wei & Andrew Lim. (2015) A bidirectional building approach for the 2D constrained guillotine knapsack packing problem. European Journal of Operational Research 242:1, pages 63-71.
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Mohsen Afsharian, Ali Niknejad & Gerhard Wäscher. (2014) A heuristic, dynamic programming-based approach for a two-dimensional cutting problem with defects. OR Spectrum 36:4, pages 971-999.
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Mauro Russo, Antonio Sforza & Claudio Sterle. (2013) An improvement of the knapsack function based algorithm of Gilmore and Gomory for the unconstrained two-dimensional guillotine cutting problem. International Journal of Production Economics 145:2, pages 451-462.
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Horacio Hideki Yanasse & Reinaldo Morabito. (2013) Modelos lineares e não lineares inteiros para problemas da mochila bidimensional restrita a 2 estágios. Production 23:4, pages 887-896.
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Yaodong Cui. (2012) A new dynamic programming procedure for three-staged cutting patterns. Journal of Global Optimization 55:2, pages 349-357.
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Yaodong Cui. (2012) Fast heuristic for constrained homogenous T-shape cutting patterns. Applied Mathematical Modelling 36:8, pages 3696-3711.
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Y Cui & Q Chen. (2011) Simple heuristic for the constrained two-dimensional cutting problem. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 226:3, pages 565-572.
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Yaodong Cui & Yuli Yang. (2011) A recursive branch-and-bound algorithm for constrained homogenous T-shape cutting patterns. Mathematical and Computer Modelling 54:5-6, pages 1320-1333.
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Urs Buehlmann, R. Edward Thomas & Xiaoqui Zuo. (2011) Cost minimization through optimized raw material quality composition. Robotics and Computer-Integrated Manufacturing 27:4, pages 746-754.
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Masao Sugi, Yusuke Shiomi, Tsuyoshi Okubo, Kazuyoshi Inoue & Jun Ota. (2010) A Solution for 2D Rectangular Cutting Stock Problems with 3-Stage Guillotine-Cutting Constraint. International Journal of Automation Technology 4:5, pages 461-468.
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Reinaldo Morabito & Vitória Pureza. (2008) A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem. Annals of Operations Research 179:1, pages 297-315.
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X. Song, C.B. Chu, R. Lewis, Y.Y. Nie & J. Thompson. (2010) A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting. European Journal of Operational Research 202:2, pages 368-378.
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Francis J. Vasko & Christopher L. Bartkowski. (2009) Using Wang's two‐dimensional cutting stock algorithm to optimally solve difficult problems. International Transactions in Operational Research 16:6, pages 829-838.
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Andreas Bortfeldt & Tobias Winter. (2009) A genetic algorithm for the two‐dimensional knapsack problem with rectangular pieces. International Transactions in Operational Research 16:6, pages 685-713.
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M. Hifi, R. M’Hallah & T. Saadi. (2007) Approximate and exact algorithms for the double-constrained two-dimensional guillotine cutting stock problem. Computational Optimization and Applications 42:2, pages 303-326.
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Yuanyan Chen. (2007) A recursive algorithm for constrained two-dimensional cutting problems. Computational Optimization and Applications 41:3, pages 337-348.
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Yaodong Cui & Zhiyong Liu. (2007) T-shape homogenous block patterns for the two-dimensional cutting problem. Journal of Global Optimization 41:2, pages 267-281.
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Horacio Hideki Yanasse, Reinaldo Morabito & Marcos Nereu Arenales. 2008. Intelligent Decision Support. Intelligent Decision Support 69 88 .
Yaodong Cui & Xianquan Zhang. (2007) Two-stage general block patterns for the two-dimensional cutting problem. Computers & Operations Research 34:10, pages 2882-2893.
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Yaodong Cui. (2007) Exact algorithm for generating two-segment cutting patterns of punched strips. Applied Mathematical Modelling 31:9, pages 1865-1873.
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Reinaldo Morabito & Vitória Pureza. (2007) Geração de padrões de cortes bidimensionais guilhotinados restritos via programação dinâmica e busca em grafo-e/ou. Production 17:1, pages 33-51.
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Yaodong Cui. (2007) Simple block patterns for the two-dimensional cutting problem. Mathematical and Computer Modelling 45:7-8, pages 943-953.
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Yaodong Cui & Jun Ji. (2006) A recursive algorithm for generating homogeneous T-shape cutting patterns. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 220:11, pages 1767-1774.
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Tuğba Saraç & Müjgan Sağır Özdemir. 2003. Developments in Applied Artificial Intelligence. Developments in Applied Artificial Intelligence 41 51 .
Ramón Alvarez-Valdés, Antonio Parajón & Jose’e Manuel Tamarit. (2002) A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems. Computers & Operations Research 29:7, pages 925-947.
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Rejane Joas Silveira & Reinaldo Morabito. (2002) Um método heurístico baseado em programação dinâmica para o problema de corte bidimensional guilhotinado restrito. Gestão & Produção 9:1, pages 78-92.
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V‐D. Cung, M. Hifi & B. Le Cun. (2006) Constrained two‐dimensional cutting stock problems a best‐first branch‐and‐bound algorithm. International Transactions in Operational Research 7:3, pages 185-210.
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