Rectangle blanket problem: Binary integer linear programming formulation and solution algorithms
Author
Abstract
Suggested Citation
DOI: 10.1016/j.ejor.2019.02.004
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
- Cherri, Luiz H. & Mundim, Leandro R. & Andretta, Marina & Toledo, Franklina M.B. & Oliveira, José F. & Carravilla, Maria Antónia, 2016. "Robust mixed-integer linear programming models for the irregular strip packing problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 570-583.
- 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.
- J. Bennell & G. Scheithauer & Y. Stoyan & T. Romanova, 2010. "Tools of mathematical modeling of arbitrary object packing problems," Annals of Operations Research, Springer, vol. 179(1), pages 343-368, September.
- A. Charnes & W. W. Cooper, 1962. "Systems Evaluation and Repricing Theorems," Management Science, INFORMS, vol. 9(1), pages 33-49, October.
- François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
- Hadjiconstantinou, Eleni & Christofides, Nicos, 1995. "An exact algorithm for general, orthogonal, two-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 83(1), pages 39-56, May.
- P. Y. Wang, 1983. "Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems," Operations Research, INFORMS, vol. 31(3), pages 573-586, June.
- Haessler, Robert W. & Sweeney, Paul E., 1991. "Cutting stock problems and solution procedures," European Journal of Operational Research, Elsevier, vol. 54(2), pages 141-150, September.
- Alvarez-Valdes, R. & Martinez, A. & Tamarit, J.M., 2013. "A branch & bound algorithm for cutting and packing irregularly shaped pieces," International Journal of Production Economics, Elsevier, vol. 145(2), pages 463-477.
- Oliveira, Jose Fernando & Wascher, Gerhard, 2007. "Cutting and Packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1106-1108, December.
- A. Pessoa & R. Sadykov & E. Uchoa & F. Vanderbeck, 2018. "Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 339-360, May.
- Y. Stoyan & T. Romanova & G. Scheithauer & A. Krivulya, 2011. "Covering a polygonal region by rectangles," Computational Optimization and Applications, Springer, vol. 48(3), pages 675-695, April.
- Beasley, J. E., 2004. "A population heuristic for constrained two-dimensional non-guillotine cutting," European Journal of Operational Research, Elsevier, vol. 156(3), pages 601-627, August.
- Gomes, A. Miguel & Oliveira, Jose F., 2006. "Solving Irregular Strip Packing problems by hybridising simulated annealing and linear programming," European Journal of Operational Research, Elsevier, vol. 171(3), pages 811-829, June.
- J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
- Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
- Bennell, Julia A. & Oliveira, Jose F., 2008. "The geometry of nesting problems: A tutorial," European Journal of Operational Research, Elsevier, vol. 184(2), pages 397-415, January.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Abraham, Gyula & Dosa, Gyorgy & Hvattum, Lars Magnus & Olaj, Tomas Attila & Tuza, Zsolt, 2023. "The board packing problem," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1056-1073.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.
- Igor Kierkosz & Maciej Luczak, 2014. "A hybrid evolutionary algorithm for the two-dimensional packing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(4), pages 729-753, December.
- José Fernando Gonçalves & Mauricio G. C. Resende, 2011. "A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 180-201, August.
- 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.
- Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
- Leao, Aline A.S. & Toledo, Franklina M.B. & Oliveira, José Fernando & Carravilla, Maria Antónia & Alvarez-Valdés, Ramón, 2020. "Irregular packing problems: A review of mathematical models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 803-822.
- Hadjiconstantinou, Eleni & Iori, Manuel, 2007. "A hybrid genetic algorithm for the two-dimensional single large object placement problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1150-1166, December.
- Akang Wang & Christopher L. Hanselman & Chrysanthos E. Gounaris, 2018. "A customized branch-and-bound approach for irregular shape nesting," Journal of Global Optimization, Springer, vol. 71(4), pages 935-955, August.
- Silva, Elsa & Oliveira, José Fernando & Silveira, Tiago & Mundim, Leandro & Carravilla, Maria Antónia, 2023. "The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems," Omega, Elsevier, vol. 114(C).
- Beasley, J. E., 2004. "A population heuristic for constrained two-dimensional non-guillotine cutting," European Journal of Operational Research, Elsevier, vol. 156(3), pages 601-627, August.
- Sato, André Kubagawa & Martins, Thiago Castro & Gomes, Antonio Miguel & Tsuzuki, Marcos Sales Guerra, 2019. "Raster penetration map applied to the irregular packing problem," European Journal of Operational Research, Elsevier, vol. 279(2), pages 657-671.
- Alvarez-Valdes, R. & Parreno, F. & Tamarit, J.M., 2007. "A tabu search algorithm for a two-dimensional non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1167-1182, December.
- Wei, Lijun & Lim, Andrew, 2015. "A bidirectional building approach for the 2D constrained guillotine knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 242(1), pages 63-71.
- István Borgulya, 2019. "An EDA for the 2D knapsack problem with guillotine constraint," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 329-356, June.
- Miguel Santoro & Felipe Lemos, 2015. "Irregular packing: MILP model based on a polygonal enclosure," Annals of Operations Research, Springer, vol. 235(1), pages 693-707, December.
- R Alvarez-Valdes & F Parreño & J M Tamarit, 2005. "A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 414-425, April.
- Cherri, Luiz Henrique & Carravilla, Maria Antónia & Ribeiro, Cristina & Toledo, Franklina Maria Bragion, 2019. "Optimality in nesting problems: New constraint programming models and a new global constraint for non-overlap," Operations Research Perspectives, Elsevier, vol. 6(C).
- Goncalves, Jose Fernando, 2007. "A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1212-1229, December.
- 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.
- Sándor P. Fekete & Jörg Schepers, 2004. "A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 353-368, May.
More about this item
Keywords
Integer programming; Branch-and-price; Computer vision; Cutting /Packing; Heuristics;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:277:y:2019:i:1:p:62-83. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.