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Characterization and modelling of guillotine constraints

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  • Ben Messaoud, Said
  • Chu, Chengbin
  • Espinouse, Marie-Laure

Abstract

This paper focuses on guillotine cuts which often arise in real-life cutting stock problems. In order to construct a solution verifying guillotine constraints, the first step is to know how to determine whether a given cutting pattern is a guillotine pattern. For this purpose, we first characterize guillotine patterns by proving a necessary and sufficient condition. Then, we propose a polynomial algorithm to check this condition. Based on this mathematical characterization of guillotine patterns, we then show that guillotine constraints can be formulated into linear inequalities. The performance of the algorithm to check guillotine cutting patterns is evaluated by means of computational results.

Suggested Citation

  • Ben Messaoud, Said & Chu, Chengbin & Espinouse, Marie-Laure, 2008. "Characterization and modelling of guillotine constraints," European Journal of Operational Research, Elsevier, vol. 191(1), pages 112-126, November.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:1:p:112-126
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    1. 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.
    2. Vera Neidlein & Andrèa C. G. Vianna & Marcos N. Arenales & Gerhard Wäscher, 2008. "The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect," FEMM Working Papers 08035, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    3. François Clautiaux & Antoine Jouglet & Aziz Moukrim, 2013. "A New Graph-Theoretical Model for the Guillotine-Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 72-86, February.
    4. 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).
    5. Pedroso, João Pedro, 2020. "Heuristics for packing semifluids," European Journal of Operational Research, Elsevier, vol. 282(3), pages 823-834.
    6. 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.
    7. Wei, Lijun & Tian, Tian & Zhu, Wenbin & Lim, Andrew, 2014. "A block-based layer building approach for the 2D guillotine strip packing problem," European Journal of Operational Research, Elsevier, vol. 239(1), pages 58-69.

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