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

AbstractThis paper introduces novel mathematical optimisation models for the 2-Dimensional guillotine Cutting Stock Problem with Variable-Sized Stock that appears in a Spanish company in the honeycomb cardboard industry. This problem mainly differs from the classical cutting stock problems in the stock, which is considered variable-sized, i.e. we have to decide the panel dimensions, width, and length. This approach is helpful in industries where the stock is produced simultaneously with the cutting process. The stock is then cut into smaller rectangular pieces that must meet the customers' requirements, such as the type of item, dimensions, demands, and technical specifications. Furthermore, in the problem tackled in this paper, the cuts are guillotine, performed side to side. The proposed mathematical models are validated using real data from the company, obtaining results that drastically reduce the produced material and leftovers, reducing operation times and economic costs.Keywords: Cutting stock problem2-dimensional cuttingvariable-sized stockmixed integer linear optimisationcardboard industry AcknowledgmentsThe authors would like to thank the company managers for providing us with real data and for giving us insight into the company's current operation.Data availability statementDue to the nature of the research, due to commercial supporting not all data is available. We refer the readers to Terán-Viadero, Alonso-Ayuso, and Martín-Campo (Citation2023) where for six instances, input data and results obtained are reported.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work has been supported by grant PID2021-122640OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ‘ERDF A way of making Europe’.Notes on contributorsPaula Terán-ViaderoPaula Terán-Viadero is a PhD student who received her Master's degree in 2019 in Mathematical Engineering from the Complutense University of Madrid (UCM), Spain. She specialised in operations research in 2019 when she was part of the Statistics and Operational Research department in the Faculty of Mathematical Sciences at UCM, developing optimisation models for a company in the hospitality sector. Since then, she has worked in the private sector, developing integer linear mathematical optimisation models to solve problems arising from real-world applications.Antonio Alonso-AyusoAntonio Alonso-Ayuso received his PhD in Mathematics from the Complutense University of Madrid, Spain, in 1997. He is currently a Full Professor in Statistics and Operational Research at Rey Juan Carlos University, Spain. His main research interests include linear and integer mathematical optimisation, decision models, and stochastic optimisation applied to combinatorial problems. He has developed several projects jointly with companies in different sectors (steel, oil and paper, among others).F. Javier Martín-CampoF. Javier Martín-Campo received his PhD from the Rey Juan Carlos University, Spain, in 2010. He is currently an Associate Professor in Statistics and Operational Research at Complutense University of Madrid, Spain. His main research interests include Operational Research, particularly Mathematical Programming (Integer, Nonlinear), Decision Aid Models for commercial and humanitarian logistics and heuristics/metaheuristics. He has worked on several projects for different sectors: air traffic management, steel, and paper, among others.