The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches (original) (raw)
Abstract
Different variations of the classic cutting stock problem (CSP) have emerged and presented increasingly complex challenges for scientists and researchers. One of these variations, which is the central subject of this work, is the two-dimensional cutting stock problem with usable leftovers (2D-CSPUL). In these problems, leftovers can be generated to reduce waste. This technique has great practical importance for many companies, with a strong economic and environmental impact. In this paper, a non-linear mathematical model and its linearization are proposed to represent the 2D-CSPUL. Due to the complexity of the model, a heuristic procedure was also proposed. Computational tests were performed with instances from the literature and randomly generated instances. The results demonstrate that the proposed model and the heuristic procedure satisfactorily solve the problem, proving to be adequate and beneficial tools when applied to real situations.
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Availability of data and material
The full description of all instances used in the computational tests can be found at http://data.mendeley.com/datasets/ddc79swng4/1.
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Funding
This research was funded by the São Paulo Research Foundation (Fundação de Amparo à Pesquisa do Estado de São Paulo) FAPESP (Grant Numbers 2019/25041-8, 2018/16600-0, 2018/07240-0 and 2016/01860-1) and the National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico) CNPq (Grant Numbers 317460/2021-8, 421130/2018-0 and 306558/2018-1). This work is partially financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia, I.P., within project POCI-01-0145-FEDER-029609.
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Authors and Affiliations
- São Paulo State University (UNESP), Bauru, Brazil
Douglas Nogueira do Nascimento & Adriana Cristina Cherri - University of Porto, Porto, Portugal
José Fernando Oliveira
Authors
- Douglas Nogueira do Nascimento
- Adriana Cristina Cherri
- José Fernando Oliveira
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Correspondence toDouglas Nogueira do Nascimento.
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Appendix: Instances from Andrade et al. (2016)
Appendix: Instances from Andrade et al. ([2016](/article/10.1007/s12351-022-00735-9#ref-CR2 "Andrade R, Birgin EG, Morabito R (2016) Two-stage two-dimensional guillotine cutting stock problems with usable leftover. Int Trans Oper Res 23:121–145.
https://doi.org/10.1111/itor.12077
"))See Table 18.
Table 18 Description of the instances from Andrade et al. ([2016](/article/10.1007/s12351-022-00735-9#ref-CR2 "Andrade R, Birgin EG, Morabito R (2016) Two-stage two-dimensional guillotine cutting stock problems with usable leftover. Int Trans Oper Res 23:121–145. https://doi.org/10.1111/itor.12077
"))
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do Nascimento, D.N., Cherri, A.C. & Oliveira, J.F. The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches.Oper Res Int J 22, 5363–5403 (2022). https://doi.org/10.1007/s12351-022-00735-9
- Received: 14 July 2021
- Revised: 24 June 2022
- Accepted: 22 July 2022
- Published: 06 August 2022
- Version of record: 06 August 2022
- Issue date: November 2022
- DOI: https://doi.org/10.1007/s12351-022-00735-9