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A MIP-CP based approach for two- and three-dimensional cutting problems with staged guillotine cuts

Author

Listed:
  • Oliviana Xavier Nascimento

    (Federal University of Goiás)

  • Thiago Alves Queiroz

    (Federal University of Goiás)

  • Leonardo Junqueira

    (University of São Paulo)

Abstract

This work presents guillotine constraints for two- and three-dimensional cutting problems. These problems look for a subset of rectangular items of maximum value that can be cut from a single rectangular container. Guillotine constraints seek to ensure that items are arranged in such a way that cuts from one edge of the container to the opposite edge completely separate them. In particular, we consider the possibility of 2, 3, and 4 cutting stages in a predefined sequence. These constraints are considered within a two-level iterative approach that combines the resolution of integer linear programming and constraint programming models. Experiments with instances of the literature are carried out, and the results show that the proposed approach can solve in less than 500 s approximately 60% and 50% of the instances for the two- and three-dimensional cases, respectively. For the two-dimensional case, in comparison with the recent literature, it was possible to improve the upper bound for 16% of the instances.

Suggested Citation

  • Oliviana Xavier Nascimento & Thiago Alves Queiroz & Leonardo Junqueira, 2022. "A MIP-CP based approach for two- and three-dimensional cutting problems with staged guillotine cuts," Annals of Operations Research, Springer, vol. 316(2), pages 805-835, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-019-03466-x
    DOI: 10.1007/s10479-019-03466-x
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    References listed on IDEAS

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    1. 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.
    2. Tobias Fanslau & Andreas Bortfeldt, 2010. "A Tree Search Algorithm for Solving the Container Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 222-235, May.
    3. Andreas Bortfeldt & Sabine Jungmann, 2012. "A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint," Annals of Operations Research, Springer, vol. 196(1), pages 53-71, July.
    4. Alyne Toscano & Socorro Rangel & Horacio Hideki Yanasse, 2017. "A heuristic approach to minimize the number of saw cycles in small-scale furniture factories," Annals of Operations Research, Springer, vol. 258(2), pages 719-746, November.
    5. 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.
    6. Baldacci, Roberto & Boschetti, Marco A., 2007. "A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1136-1149, December.
    7. 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.
    8. 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.
    9. 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.
    10. Puchinger, Jakob & Raidl, Gunther R., 2007. "Models and algorithms for three-stage two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1304-1327, December.
    11. David Pisinger & Mikkel Sigurd, 2007. "Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 36-51, February.
    12. Velasco, André Soares & Uchoa, Eduardo, 2019. "Improved state space relaxation for constrained two-dimensional guillotine cutting problems," European Journal of Operational Research, Elsevier, vol. 272(1), pages 106-120.
    13. Reinaldo Morabito & Vitória Pureza, 2010. "A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem," Annals of Operations Research, Springer, vol. 179(1), pages 297-315, September.
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