Strip based compact formulation for two-dimensional guillotine cutting problems

Rodrigues, Carlos Diego; Cherri, Adriana Cristina; Araújo, Silvio Alexandre de

doi:10.1016/j.cor.2022.106044

Cited by 7 publications

(4 citation statements)

References 42 publications

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“…(2023) and the other from Rodrigues et al. (2023). Unfortunately, it was past the time to include them in our experiments.…”

Section: Introductionmentioning

confidence: 97%

“…Silva et al (2023) propose a floating-cuts paradigm for which formulations for many problem variants (supporting guillotine and non-guillotine patterns, limited and unlimited stages) are written and tested. Rodrigues et al (2023) also present a flexible formulation (supporting limited and unlimited stages, exact and non-exact patterns), and their focus is a restricted heuristic version of their model. Besides these new formulations, at least two new surveys worth mentioning were published by Oliveira et al (2023) (reviewing the whole area of two-dimensional rectangular cutting and packing) and Iori et al (2021) (focusing on exact methods for two-dimensional cutting and packing) and also an instance library (2DPacklib) presented in Iori et al (2022).…”

Section: Introductionmentioning

confidence: 99%

“…While this paper was going through the review and publishing process, other works related to ours and worth mentioning got published. These include two new formulations capable of solving the C2GCP, one from Silva et al (2023) and the other from Rodrigues et al (2023). Unfortunately, it was past the time to include them in our experiments.…”

Section: Introductionmentioning

confidence: 99%

“…Rodrigues et al. (2023) also present a flexible formulation (supporting limited and unlimited stages, exact and non‐exact patterns), and their focus is a restricted heuristic version of their model. Besides these new formulations, at least two new surveys worth mentioning were published by Oliveira et al.…”

Section: Introductionmentioning

confidence: 99%

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Comparative analysis of mathematical formulations for the two‐dimensional guillotine cutting problem

Becker

Martin

Araújo

et al. 2023

Int Trans Operational Res

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About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo‐polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch‐and‐bound time thanks to the symmetries broken by the hybridisation.

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“…(2023) and the other from Rodrigues et al. (2023). Unfortunately, it was past the time to include them in our experiments.…”

Section: Introductionmentioning

confidence: 97%