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A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem

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  • Reinaldo Morabito
  • Vitória Pureza

Abstract

In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/or-graph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method’s performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:297-315:10.1007/s10479-008-0457-4
    DOI: 10.1007/s10479-008-0457-4
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    Cited by:

    1. Carlos V. G. C. Lima & Fábio Protti & Dieter Rautenbach & Uéverton S. Souza & Jayme L. Szwarcfiter, 2018. "And/or-convexity: a graph convexity based on processes and deadlock models," Annals of Operations Research, Springer, vol. 264(1), pages 267-286, May.
    2. 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.
    3. Russo, Mauro & Sforza, Antonio & Sterle, Claudio, 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, Elsevier, vol. 145(2), pages 451-462.
    4. Krzysztof Fleszar, 2016. "An Exact Algorithm for the Two-Dimensional Stage-Unrestricted Guillotine Cutting/Packing Decision Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 703-720, November.
    5. 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.
    6. 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.
    7. 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.

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