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Cutting stock problem with usable leftovers: A review

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  • Senergues, Victor
  • Brahimi, Nadjib
  • Cherri, Adriana Cristina
  • Klein, François
  • Péton, Olivier

Abstract

This article presents a comprehensive literature review of the Cutting Stock Problem with Usable Leftovers (CSPUL). The most recent review on this topic dates to 2014, covering articles published before 2013. Since then, the number of publications on CSPUL has increased significantly, driven by new applications and more efficient solution approaches. We analyze fifty two relevant articles from twenty four different journals, focusing on works published after 2008 while acknowledging foundational contributions from the 1980s and 1990s. This review categorizes variations of CSPUL based on their dimensions (1D, 2D, and 3D), planning period characteristics (single-period and multi-period), objective functions, and solution methods. The article provides a detailed summary of the key features in the mathematical models and solution methods proposed in these studies. Additionally, it highlights several industrial applications of CSPUL, illustrating its practical relevance. Through this analysis, we identify important applications and propose promising directions for future research. The findings and insights presented here have practical implications for optimizing resource utilization and promoting sustainability in industries facing cutting challenges.

Suggested Citation

  • Senergues, Victor & Brahimi, Nadjib & Cherri, Adriana Cristina & Klein, François & Péton, Olivier, 2026. "Cutting stock problem with usable leftovers: A review," European Journal of Operational Research, Elsevier, vol. 328(1), pages 1-14.
    • Handle: RePEc:eee:ejores:v:328:y:2026:i:1:p:1-14
    DOI: 10.1016/j.ejor.2025.03.014
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    1. E Silva & F Alvelos & J M Valério de Carvalho, 2014. "Integrating two-dimensional cutting stock and lot-sizing problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(1), pages 108-123, January.
    2. Silva, Elsa & Alvelos, Filipe & Valério de Carvalho, J.M., 2010. "An integer programming model for two- and three-stage two-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 205(3), pages 699-708, September.
    3. Cheng, C. H. & Feiring, B. R. & Cheng, T. C. E., 1994. "The cutting stock problem -- a survey," International Journal of Production Economics, Elsevier, vol. 36(3), pages 291-305, October.
    4. Cherri, Adriana Cristina & Cherri, Luiz Henrique & Oliveira, Beatriz Brito & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "A stochastic programming approach to the cutting stock problem with usable leftovers," European Journal of Operational Research, Elsevier, vol. 308(1), pages 38-53.
    5. Cui, Yaodong & Yang, Yuli, 2010. "A heuristic for the one-dimensional cutting stock problem with usable leftover," European Journal of Operational Research, Elsevier, vol. 204(2), pages 245-250, July.
    6. Santiago V. Ravelo & Cláudio N. Meneses & Maristela O. Santos, 2020. "Meta-heuristics for the one-dimensional cutting stock problem with usable leftover," Journal of Heuristics, Springer, vol. 26(4), pages 585-618, August.
    7. Supphakorn Sumetthapiwat & Boonyarit Intiyot & Chawalit Jeenanunta, 2020. "A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 35(2), pages 273-288.
    8. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    9. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki & Poldi, Kelly Cristina & Gonçalves Vianna, Andréa Carla, 2014. "The one-dimensional cutting stock problem with usable leftovers – A survey," European Journal of Operational Research, Elsevier, vol. 236(2), pages 395-402.
    10. Claudio Arbib & Fabrizio Marinelli & Fabrizio Rossi & Francesco Di Iorio, 2002. "Cutting and Reuse: An Application from Automobile Component Manufacturing," Operations Research, INFORMS, vol. 50(6), pages 923-934, December.
    11. Douglas Nogueira Nascimento & Adriana Cristina Cherri & José Fernando Oliveira, 2022. "The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches," Operational Research, Springer, vol. 22(5), pages 5363-5403, November.
    12. François Clautiaux & Ruslan Sadykov & François Vanderbeck & Quentin Viaud, 2019. "Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 265-297, September.
    13. Karen Rocha Coelho & Adriana Cristina Cherri & Edméa Cassia Baptista & Charbel José Chiappetta Jabbour & Edilaine Martins Soler, 2017. "Sustainable operations: The cutting stock problem with usable leftovers from a sustainable perspective," Post-Print hal-02000703, HAL.
    14. Alexander Abuabara & Reinaldo Morabito, 2009. "Cutting optimization of structural tubes to build agricultural light aircrafts," Annals of Operations Research, Springer, vol. 169(1), pages 149-165, July.
    15. Ricardo Andrade & Ernesto G Birgin & Reinaldo Morabito & Débora P Ronconi, 2014. "MIP models for two-dimensional non-guillotine cutting problems with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(11), pages 1649-1663, November.
    16. Gradisar, Miro & Kljajic, Miroljub & Resinovic, Gortan & Jesenko, Joze, 1999. "A sequential heuristic procedure for one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 114(3), pages 557-568, May.
    17. Trkman, Peter & Gradisar, Miro, 2007. "One-dimensional cutting stock optimization in consecutive time periods," European Journal of Operational Research, Elsevier, vol. 179(2), pages 291-301, June.
    18. Chengbin Chu & Julien Antonio, 1999. "Approximation Algorithms to Solve Real-Life Multicriteria Cutting Stock Problems," Operations Research, INFORMS, vol. 47(4), pages 495-508, August.
    19. Silvano Martello & Michele Monaci & Daniele Vigo, 2003. "An Exact Approach to the Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 310-319, August.
    20. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    21. Yaodong Cui & Xiang Song & Yan Chen & Yi-Ping Cui, 2017. "New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 269-280, March.
    22. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    23. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    24. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    25. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki, 2009. "The one-dimensional cutting stock problem with usable leftover - A heuristic approach," European Journal of Operational Research, Elsevier, vol. 196(3), pages 897-908, August.
    26. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.
    27. Joaquim L. Viegas & Susana M. Vieira & Elsa M.P. Henriques & João M.C. Sousa, 2016. "Heuristics for three-dimensional steel cutting with usable leftovers considering large time periods," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(4), pages 431-454.
    28. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    29. Luka Tomat & Mirko Gradišar, 2017. "One-dimensional stock cutting: optimization of usable leftovers in consecutive orders," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 473-489, June.
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