cutting in the cardboard industry | F. Javier Martín-Campo

Cutting processes play a fundamental role in the cardboard and packaging industry, where large sheets or rolls of material must be transformed into smaller items that meet diverse customer specifications. The design of cutting patterns and the associated decision-making process have a direct impact on production efficiency, material utilization, and operational costs. Well-designed cutting patterns allow manufacturers to maximize the use of available material, significantly reducing waste, while also improving throughput and sustainability. As raw material costs and environmental concerns continue to grow, optimizing cutting decisions has become a key factor in enhancing competitiveness and ensuring more efficient and responsible production processes.

In (Terán-Viadero et al., 2023), a mathematical optimization model is introduced for a novel problem in the cutting stock literature, namely the two-dimensional variable-sized cutting stock problem. Unlike classical cutting stock settings, this problem allows the production of stock sheets with variable length and width, after which cutting patterns are defined on the produced stock to meet customer orders. The model focuses on selecting cutting patterns that satisfy demand while avoiding the use of explicit assignment variables (usual in the literature), as this information is embedded directly into model parameters. This modeling choice significantly reduces computational times and improves scalability. To preserve tractability, the formulation considers cutting patterns containing at most two items, achieving an effective balance between model complexity and solution quality. The proposed approach is validated using real-world datasets published in (Terán-Viadero et al., 2023).

Building on this work, (Terán-Viadero et al., 2024) presents an extended formulation that generalizes the problem by allowing cutting patterns to include any number of items, provided that the resulting pattern is geometrically feasible. This extension broadens the applicability of the model and enables a more comprehensive representation of practical cutting processes in the cardboard industry. The generalized model has been validated using additional datasets made publicly available in (Terán-Viadero et al., 2024), demonstrating its robustness and suitability for more complex industrial scenarios.

References

2024

Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem

Paula Terán-Viadero, Antonio Alonso-Ayuso, and F. Javier Martín-Campo

European Journal of Operational Research, Nov 2024

DOI Bib

@article{TeranViadero2024,
  title = {Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem},
  volume = {319},
  issn = {0377-2217},
  url = {http://dx.doi.org/10.1016/j.ejor.2024.06.022},
  doi = {10.1016/j.ejor.2024.06.022},
  number = {1},
  journal = {European Journal of Operational Research},
  publisher = {Elsevier BV},
  author = {Terán-Viadero, Paula and Alonso-Ayuso, Antonio and Martín-Campo, F. Javier},
  year = {2024},
  month = nov,
  pages = {303–315},
  google_scholar_id = {KlAtU1dfN6UC},
  dimensions = {true}
}

Dataset used in article "Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem"

Paula Terán-Viadero, Antonio Alonso-Ayuso, and F. Javier Martín-Campo

Nov 2024

DOI Bib

@misc{TeranViaderoDS2024,
  doi = {10.5281/ZENODO.10555353},
  url = {https://zenodo.org/doi/10.5281/zenodo.10555353},
  author = {Terán-Viadero, Paula and Alonso-Ayuso, Antonio and Martín-Campo, F. Javier},
  title = {Dataset used in article "Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem"},
  publisher = {Zenodo},
  year = {2024},
  copyright = {Creative Commons Attribution 4.0 International},
  google_scholar_id = {M3ejUd6NZC8C}
}

2023

A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry

Paula Terán-Viadero, Antonio Alonso-Ayuso, and F. Javier Martín-Campo

International Journal of Production Research, Nov 2023

DOI Bib

@article{TeranViadero2023,
  title = {A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry},
  volume = {62},
  issn = {1366-588X},
  url = {http://dx.doi.org/10.1080/00207543.2023.2279129},
  doi = {10.1080/00207543.2023.2279129},
  number = {1–2},
  journal = {International Journal of Production Research},
  publisher = {Informa UK Limited},
  author = {Terán-Viadero, Paula and Alonso-Ayuso, Antonio and Martín-Campo, F. Javier},
  year = {2023},
  month = nov,
  pages = {483–500},
  google_scholar_id = {3fE2CSJIrl8C},
  dimensions = {true}
}

Dataset used in article "A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry"

Paula Terán-Viadero, Antonio Alonso-Ayuso, and F. Javier Martín-Campo

Nov 2023

DOI Bib

@misc{TeranViaderoDS2023,
  doi = {10.5281/ZENODO.8033003},
  url = {https://zenodo.org/doi/10.5281/zenodo.8033003},
  author = {Terán-Viadero, Paula and Alonso-Ayuso, Antonio and Martín-Campo, F. Javier},
  title = {Dataset used in article "A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry"},
  publisher = {Zenodo},
  year = {2023},
  copyright = {Creative Commons Attribution 4.0 International},
  google_scholar_id = {YOwf2qJgpHMC}
}