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An AND/OR-graph approach to the solution of two-dimensional non-guillotine cutting problems

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  • Arenales, Marcos
  • Morabito, Reinaldo

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  • Arenales, Marcos & Morabito, Reinaldo, 1995. "An AND/OR-graph approach to the solution of two-dimensional non-guillotine cutting problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 599-617, August.
    • Handle: RePEc:eee:ejores:v:84:y:1995:i:3:p:599-617
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    References listed on IDEAS

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    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Dowsland, Kathryn A. & Dowsland, William B., 1992. "Packing problems," European Journal of Operational Research, Elsevier, vol. 56(1), pages 2-14, January.
    3. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    4. Dowsland, Kathryn A., 1987. "An exact algorithm for the pallet loading problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 78-84, July.
    5. Biro, Milos & Boros, Endre, 1984. "Network flows and non-guillotine cutting patterns," European Journal of Operational Research, Elsevier, vol. 16(2), pages 215-221, May.
    6. Dowsland, Kathryn A., 1990. "Efficient automated pallet loading," European Journal of Operational Research, Elsevier, vol. 44(2), pages 232-238, January.
    7. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    8. 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.
    9. Morabito, R. N. & Arenales, M. N. & Arcaro, V. F., 1992. "An and--or-graph approach for two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 58(2), pages 263-271, April.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Lins, Lauro & Lins, Sostenes & Morabito, Reinaldo, 2002. "An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container," European Journal of Operational Research, Elsevier, vol. 141(2), pages 421-439, September.
    5. 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.
    6. 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.
    7. Bhattacharya, Subir & Roy, Rahul & Bhattacharya, Sumita, 1998. "An exact depth-first algorithm for the pallet loading problem," European Journal of Operational Research, Elsevier, vol. 110(3), pages 610-625, November.
    8. Martins, Gustavo H.A. & Dell, Robert F., 2008. "Solving the pallet loading problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 429-440, January.
    9. Cintra, G.F. & Miyazawa, F.K. & Wakabayashi, Y. & Xavier, E.C., 2008. "Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 61-85, November.
    10. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    11. 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.
    12. Yanasse, Horacio Hideki & Pinto Lamosa, Maria Jose, 2007. "An integrated cutting stock and sequencing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1353-1370, December.
    13. G, Young-Gun & Kang, Maing-Kyu, 2001. "A fast algorithm for two-dimensional pallet loading problems of large size," European Journal of Operational Research, Elsevier, vol. 134(1), pages 193-202, October.
    14. Hoto, Robinson & Arenales, Marcos & Maculan, Nelson, 2007. "The one dimensional Compartmentalised Knapsack Problem: A case study," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1183-1195, December.
    15. 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).
    16. 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.
    17. E G Birgin & R D Lobato & R Morabito, 2010. "An effective recursive partitioning approach for the packing of identical rectangles in a rectangle," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(2), pages 306-320, February.
    18. L Lins & S Lins & R Morabito, 2003. "An L-approach for packing (ℓ, w)-rectangles into rectangular and L-shaped pieces," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(7), pages 777-789, July.
    19. Sándor P. Fekete & Jörg Schepers & Jan C. van der Veen, 2007. "An Exact Algorithm for Higher-Dimensional Orthogonal Packing," Operations Research, INFORMS, vol. 55(3), pages 569-587, June.
    20. Morabito, Reinaldo & Arenales, Marcos N., 1996. "Staged and constrained two-dimensional guillotine cutting problems: An AND/OR-graph approach," European Journal of Operational Research, Elsevier, vol. 94(3), pages 548-560, November.
    21. Gonçalves, José Fernando & Wäscher, Gerhard, 2020. "A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects," European Journal of Operational Research, Elsevier, vol. 286(3), pages 867-882.

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