How to cite this paper
APA: Francescatto, M., Júnior, A & Araújo, O. (2025). Packing layout added value in sheet metal laser cutting operations considering raw material reuse. International Journal of Industrial Engineering Computations, 16(2), 335-356.
Chicago/Turabian: Francescatto, M., Júnior, A & Araújo, O. 2025. "Packing layout added value in sheet metal laser cutting operations considering raw material reuse." International Journal of Industrial Engineering Computations 16, no. 2 (2025): 335-356.
AMA: Francescatto, M., Júnior, A & Araújo, O. Packing layout added value in sheet metal laser cutting operations considering raw material reuse. International Journal of Industrial Engineering Computations. 2025;16(2):335-356.
References
Adalarasan, R., Santhanakumar, M., & Rajmohan, M. (2015). Optimization of laser cutting parameters for Al6061/SiCp/Al2O3 composite using grey-based response surface methodology (GRSM). Measurement, 73, 596-606. https://doi.org/10.1016/j.measurement.2015.06.003
Ali, A., Wang, Y., & Alvarado, J. (2019). Facilitating industrial symbiosis to achieve circular economy using value-added by design: A case study in transforming the automobile industry sheet metal waste-flow into Voronoi facade systems. Journal of Cleaner Production, 234, 1033-1044. https://doi.org/10.1016/j.jclepro.2019.06.202
Alvarez-Valdés, R., Martínez, A., & Tamarit, J. M. (2013). A branch & bound algorithm for cutting and packing irregularly shaped pieces. International Journal of Production Economics, 145, 463-477. https://doi.org/10.1016/j.ijpe.2013.04.007
AMADA. (2023). REGIUS-AJ. Retrieved from https://www.amada.eu/uk-en/products/sheet-metal-machines-and-automation/laser-cutting-machines/regius-aj/. Accessed September 28, 2024.
Aşık, O. B., & Özcan, E. (2009). Bidirectional best-fit heuristic for orthogonal rectangular strip packing. Annals of Operations Research, 172, 405-427. https://doi.org/10.1007/s10479-009-0642-0
Baker, B. S., Coffman Jr, E. G., & Rivest, R. L. (1980). Orthogonal packings in two dimensions. SIAM Journal on Computing, 9, 846-855. https://doi.org/10.1137/0209064
Baldi, M. M., & Bruglieri, M. (2017). On the generalized bin packing problem. International Transactions in Operational Research, 24, 425-438. https://doi.org/10.1111/itor.12258
Beasley, J. E. (1985). Exact two-dimensional non-guillotine cutting tree search procedure. Operations Research, 33, 49-64. https://www.jstor.org/stable/170866
Bengtsson, B. E. (1982). Packing rectangular pieces – A heuristic approach. The Computer Journal, 25, 353-357. https://doi.org/10.1093/comjnl/25.3.353
Bennel, J., & Oliveira, J. (2008). The geometry of nesting problems: A tutorial. European Journal of Operational Research, 184, 397-415. https://doi.org/10.1016/j.ejor.2006.11.038
Berkey, J. O., & Wang, P. Y. (1987). Two-dimensional finite bin-packing algorithms. Journal of the Operational Research Society, 38, 423-429. https://doi.org/10.2307/2582731
Berkmanns, J., & Faerber, M. (2008). Laser cutting LASERLINE®. Retrieved from https://www.boconline.co.uk/en/images/laser-cutting_tcm410-39553.pdf
Bertolini, M., Mezzogori, D., & Zammori, F. (2024). Hybrid heuristic for the one-dimensional cutting stock problem with usable leftovers and additional operating constraints. International Journal of Industrial Engineering Computations, 15(1), 149-170. https://doi.org/10.5267/j.ijiec.2023.10.006
Bortfeldt, A., & Jungmann, S. (2012). A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint. Annals of Operations Research, 196, 53-71. https://doi.org/10.1007/s10479-012-1084-7
Brandão, F., & Pedroso, J. P. (2014). Fast pattern-based algorithms for cutting stock. Computers & Operations Research, 48, 69-80. https://doi.org/10.1016/j.cor.2014.03.003
Buchwald, T., & Scheithauer, G. (2016). Upper bounds for heuristic approaches to the strip packing problem. International Transactions in Operational Research, 23, 93-111. https://doi.org/10.1111/itor.12100
Buer, S. V., Stranghagen, J. O., & Chan, F. T. S. (2018). The link between Industry 4.0 and lean manufacturing: Mapping current research and establishing a research agenda. International Journal of Production Research, 56, 2924-2940. https://doi.org/10.1080/00207543.2018.1442945
Burke, E. K., Kendal, G., & Whitwell, G. (2004). A new placement heuristic for the orthogonal stock-cutting problem. Operations Research, 52, 655-671. https://doi.org/10.1287/opre.1040.0109
Bystronic. (2023). BySmart Fiber: Smart access for laser cutting of metal. Retrieved from https://www.bystronic.com/usa/en-us/l/laser-cutting-metal-bysmart-fiber. Accessed September 28, 2024.
Çaidas, U., & Hasçalik, A. (2008). Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics. Optics & Laser Technology, 40, 987-994. https://doi.org/10.1016/j.optlastec.2008.01.004
Chazelle, B. (1983). The bottom-left bin-packing heuristic: An efficient implementation. IEEE Transactions on Computing, 100, 697-707. https://doi.org/10.1109/TC.1983.1676307
Chen, B., Wang, Y., & Yang, S. (2015). A hybrid demon algorithm for the two-dimensional orthogonal strip packing problem. Mathematical Problems in Engineering, 2015, 541931. https://doi.org/10.1155/2015/541931
Chen, W., Zhai, P., Zhu, H., & Zhang, Y. (2014). Hybrid algorithm for the two-dimensional rectangular layer-packing problem. Journal of the Operational Research Society, 65(7), 1068–1077. https://doi.org/10.1057/jors.2013.54
Chernov, N., Stoyan, Y., & Romanova, T. (2010). Mathematical model and efficient algorithms for object packing problem. Computational Geometry, 43, 535–553. https://doi.org/10.1016/j.comgeo.2009.12.003
Cherri, A. C., Arenales, M. N., & Yansse, H. H. (2013). The usable leftover one-dimensional cutting stock problem—a priority-in-use heuristic. International Transactions in Operational Research, 20, 189–199. https://doi.org/10.1111/j.1475-3995.2012.00868.x
Christofides, N., & Whitlock, C. (1977). An algorithm for two-dimensional cutting problems. Operations Research, 25, 30–44. https://www.jstor.org/stable/169545
Coffman, E., Garey, M. R., Johnson, D. S., & Tarjan, R. E. (1980). Performance bounds for level-oriented two-dimensional packing algorithms. SIAM Journal on Computing, 9, 808–826. https://doi.org/10.1137/0209062
Coffman, E. F., & Shor, P. W. (1990). Average-case analysis of cutting and packing in two dimensions. European Journal of Operational Research, 44, 134–144. https://doi.org/10.1016/0377-2217(90)90349-G
Côté, J. F., & Iori, M. (2018). The Meet-in-the-Middle Principle for Cutting and Packing. INFORMS Journal on Computing, 30, 646–661. https://doi.org/10.1287/ijoc.2018.0806
Cui, Y., Yang, L., & Cheng, Q. (2013). Heuristic for the rectangular strip packing problem with rotation of items. Computers & Operations Research, 40, 1094–1099. https://doi.org/10.1016/j.cor.2012.11.020
Cui, Y., Yang, Y., Cheng, X., & Song, P. (2008). A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem. Computers & Operations Research, 35, 1281–1291. https://doi.org/10.1016/j.cor.2006.08.011
Elsheikh, A. H., Shehabeldeen, T. A., Zhou, J., Showaib, E., & Elaziz, M. A. (2021). Prediction of laser cutting parameters for polymethylmethacrylate sheets using random vector functional link network integrated with equilibrium optimizer. Journal of Intelligent Manufacturing, 32, 1377–1388. https://doi.org/10.1007/s10845-020-01617-7
Eswaramoorthi, M., Kathiresan, G. R., Prasa, P. S. S., & Mohanram, P. V. (2011). A survey on lean practices in Indian machine tool industries. The International Journal of Advanced Manufacturing Technology, 52, 1091–1101. https://doi.org/10.1007/s00170-010-2788-y
Fanslau, T., & Bortfeldt, A. (2010). A tree search algorithm for solving the container loading problem. INFORMS Journal on Computing, 22, 222–235. https://doi.org/10.1287/ijoc.1090.0338
Francescatto, M., Neuenfeldt, A., Silva, E., Furtado, J. C., & Bromberger, D. (2023). Impact of minimum distance constraints on sheet metal waste for plasma cutting. PLOS ONE. https://doi.org/10.1371/journal.pone.0292032
Gaustad, G., Krystofik, M., Bustamente, M., & Badami, K. (2018). Circular economy strategies for mitigating critical material supply issues. Resources, Conservation & Recycling, 135, 24–33. https://doi.org/10.1016/j.resconrec.2017.08.002
Ghany, K. A., & Newishy, M. (2005). Cutting of 1.2 mm thick austenitic stainless steel sheet using pulsed and CW Nd laser. Journal of Materials Processing Technology, 168, 438–447. https://doi.org/10.1016/j.jmatprotec.2005.02.251
Gracia, C., Andrés, C., & Gracia, L. (2013). A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company. Journal of Heuristics, 19, 253–273. https://doi.org/10.1007/s10732-011-9187-x
Hifi, M., & Ouafi, R. (1998). A Best-first Branch-and-bound algorithm for orthogonal rectangular packing problems. International Transactions in Operational Research, 5(3), 345–356. https://doi.org/10.1016/S0969-6016(98)00026-4
Hopper, E. (2000). Two-dimensional packing utilizing evolutionary algorithms and other meta-heuristic methods [Ph.D. thesis].
Hopper, E., & Turton, B. (1999). A genetic algorithm for a 2D industrial packing problem. Computers & Industrial Engineering, 37(3), 375–378. https://doi.org/10.1016/S0360-8352(99)00097-2
Hopper, E., & Turton, B. C. H. (2001). Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research, 128(1), 34–57. https://doi.org/10.1016/S0377-2217(99)00357-4
Imahori, S., & Yagiura, M. (2010). The best-fit heuristic for the rectangular strip packing problem: An efficient implementation and the worst-case approximation ratio. Computers and Operations Research, 37(3), 325–333. https://doi.org/10.1016/j.cor.2009.05.008
Iori, M., de Lima, V. L., Martello, S., Miyazawa, F. K., & Monaci, M. (2021). Exact solution techniques for two-dimensional cutting and packing. European Journal of Operational Research, 289(2), 399–415. https://doi.org/10.1016/j.ejor.2020.06.050
Jasti, N. V. K., & Kodali, R. (2014). Lean production: Literature review and trends. International Journal of Production Research, 53(3), 867–885. https://doi.org/10.1080/00207543.2014.937508
Júnior, A. N., Silva, E., Francescatto, M., Rosa, C. B., & Siluk, J. (2022). The rectangular two-dimensional strip packing problem real-life practical constraints: A bibliometric overview. Computers & Operations Research, 137, 105521. https://doi.org/10.1016/j.cor.2021.105521
Kokten, E. S., & Sel, Ç. (2022). A cutting stock problem in the wood products industry: A two-stage solution approach. International Transactions in Operational Research, 29(3), 879–907. https://doi.org/10.1111/itor.12802
Kos, L., & Duhvonik, J. (2002). Cutting optimization with variable-sized stock and inventory status data. International Journal of Production Research, 40(11), 2289–2301. https://doi.org/10.1080/00207540210128161
Leung, S. C. H., & Zhang, D. (2011). A fast layer-based heuristic for non-guillotine strip packing. Expert Systems with Applications, 38(10), 13032–13042. https://doi.org/10.1016/j.eswa.2011.04.105
Liu, D., & Teng, H. (1999). An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research, 112(3), 413–420. https://doi.org/10.1016/S0377-2217(97)00437-2
Liu, K., Zhang, H., Wang, C., Li, H., Chen, Y., & Chen, Q. (2023). Robust optimization for the two-dimensional strip-packing problem with variable-sized bins. Mathematics, 11(23), 4781. https://doi.org/10.3390/math11234781
Lodi, A., Martello, S., & Vigo, D. (1999). Approximation algorithms for the oriented two-dimensional bin packing problem. European Journal of Operational Research, 112(1), 158–166. https://doi.org/10.1016/S0377-2217(97)00388-3
Madhukar, Y. K., Mullic, S., & Nath, A. K. (2016). An investigation on co-axial water-jet assisted fiber laser cutting of metal sheets. Optics and Lasers in Engineering, 77, 203–218. https://doi.org/10.1016/j.optlaseng.2015.08.003
Martello, S., Monaci, M., & Vigo, D. (2003). An exact approach to the strip-packing problem. INFORMS Journal on Computing, 15(3), 310–319. https://doi.org/10.1287/ijoc.15.3.310.16082
Nascimento, D., Alencastro, V., Quelhas, O., Caiado, R., Garza-Reyes, J., Rocha-Lona, L., & Tortorella, G. (2018). Exploring Industry 4.0 technologies to enable circular economy practices in a manufacturing context: A business model proposal. Journal of Manufacturing Technology Management, 30(3), 607–627. https://doi.org/10.1108/JMTM-03-2018-0071
Na, G.-Y., & Yang, J. (2023). Two-dimensional polygon classification and pairwise clustering for pairing in ship parts nesting. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-023-02196-z
Neuenfeldt, A. J., Francescatto, M., Araújo, O., Disconzi, D., & Stieler, G. (2023). The machining torch movement for the rectangular plasma sheet metal cut. PLoS ONE. https://doi.org/10.1371/journal.pone.0291184
Ntene, N. (2007). An algorithmic approach to the 2D oriented strip packing problem (PhD thesis).
Ntene, N., & Van Vuuren, J.H. (2009). A survey and comparison of guillotine heuristics for the 2D oriented offline strip packing problem. Discrete Optimization, 6, 174–188. https://doi.org/10.1016/j.disopt.2008.11.002
Oliveira, J. F., Neuenfeldt Jr, A., Silva, E., & Carravilla, M. A. (2016). A survey on heuristics for the two-dimensional rectangular strip packing problem. Pesquisa Operacional, 36, 197–226. https://doi.org/10.1590/0101-7438.2016.036.02.0197
Ortmann, F. G., Ntene, N., & Van Vuuren, J. H. (2010). New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems. European Journal of Operational Research, 203, 306–315. https://doi.org/10.1016/j.ejor.2009.07.024
Özcan, E., Kaiz, Z., & Drake, J. H. (2013). Bidirectional best-fit heuristic considering compound placement for two-dimensional orthogonal rectangular strip packing. Expert Systems with Applications, 40, 4035–4043. https://doi.org/10.1016/j.eswa.2013.01.005
Rajaram, N., Sheikh-Ahmad, J., & Cheraghi, S. H. (2003). C2 laser cut quality of 4130 steel. International Journal of Machine Tools & Manufacture, 43, 351–358. https://doi.org/10.1016/S0890-6955(02)00270-5
Silva, E., Oliveira, J. F., & Wäscher, G. (2014). 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems. European Journal of Operational Research, 237, 846–856. https://doi.org/10.1016/j.ejor.2014.02.059
Sweeney, P. E., & Paternoster, E. R. (1992). Cutting and packing problems: A categorized, application-orientated research bibliography. Journal of Operational Research Society, 43, 691–706. https://doi.org/10.2307/2583579
TRUMPF. (2023). 2D laser cutting machines TruLaser 1030 fiber/1040 fiber/1060 fiber. Retrieved from https://www.trumpf.com/en_INT/products/machines-systems/2d-laser-cutting-machines/trulaser-1030-fiber-1040-fiber-1060-fiber/. Accessed September 28, 2024.
Vasilyev, I., Ushakov, A. V., Zhang, D., & Ren, J. (2023). Generalized multiple strip packing problem: Formulations, applications, and solution algorithms. Computers & Industrial Engineering, 178, 109096. https://doi.org/10.1016/j.cie.2023.109096
Vinodh, S., Kumar, S. V., & Vimal, K. E. K. (2012). Implementing lean sigma in an Indian rotary switches manufacturing organization. Production Planning & Control, 25, 288–302. https://doi.org/10.1080/09537287.2012.684726
Wang, P. Y., & Valenzuela, C. L. (2001). Data set generation for rectangular placement problems. European Journal of Operational Research, 134, 378–391. https://doi.org/10.1016/S0377-2217(00)00263-0
Wang, Z., Daofang, C., & Xingyu, M. (2022). Optimization of two-dimensional irregular bin packing problem considering slit distance and free rotation of pieces. International Journal of Industrial Engineering Computations, 13(4), 491–506. https://doi.org/10.5267/j.ijiec.2022.8.001
Wäscher, G., Haußner, H., & Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research, 183, 1109–1130. https://doi.org/10.1016/j.ejor.2005.12.047
Wei, L., Tian, T., Hu, Z., & Lim, A. (2014). A block-based layer building approach for the 2D guillotine strip packing problem. European Journal of Operational Research, 239, 58–69. https://doi.org/10.1016/j.ejor.2014.04.020
Wei, L., Wang, Y., Cheng, H., & Huang, J. (2019). An open space-based heuristic for the 2D strip packing problem with unloading constraints. Applied Mathematical Modelling, 70, 67–81. https://doi.org/10.1016/j.apm.2019.01.022
Xu, J., & Yang, W. (2022). Multi-objective steel plate cutting optimization problem based on real number coding genetic algorithm. Scientific Reports, 12, 22472. https://doi.org/10.1038/s41598-022-27100-2
Yao, S., Zhang, H., Wei, L., & Liu, Q. (2025). An exact approach for the two-dimensional strip packing problem with defects. Computers & Industrial Engineering, 200(110866). https://doi.org/10.1016/j.cie.2025.110866
Ali, A., Wang, Y., & Alvarado, J. (2019). Facilitating industrial symbiosis to achieve circular economy using value-added by design: A case study in transforming the automobile industry sheet metal waste-flow into Voronoi facade systems. Journal of Cleaner Production, 234, 1033-1044. https://doi.org/10.1016/j.jclepro.2019.06.202
Alvarez-Valdés, R., Martínez, A., & Tamarit, J. M. (2013). A branch & bound algorithm for cutting and packing irregularly shaped pieces. International Journal of Production Economics, 145, 463-477. https://doi.org/10.1016/j.ijpe.2013.04.007
AMADA. (2023). REGIUS-AJ. Retrieved from https://www.amada.eu/uk-en/products/sheet-metal-machines-and-automation/laser-cutting-machines/regius-aj/. Accessed September 28, 2024.
Aşık, O. B., & Özcan, E. (2009). Bidirectional best-fit heuristic for orthogonal rectangular strip packing. Annals of Operations Research, 172, 405-427. https://doi.org/10.1007/s10479-009-0642-0
Baker, B. S., Coffman Jr, E. G., & Rivest, R. L. (1980). Orthogonal packings in two dimensions. SIAM Journal on Computing, 9, 846-855. https://doi.org/10.1137/0209064
Baldi, M. M., & Bruglieri, M. (2017). On the generalized bin packing problem. International Transactions in Operational Research, 24, 425-438. https://doi.org/10.1111/itor.12258
Beasley, J. E. (1985). Exact two-dimensional non-guillotine cutting tree search procedure. Operations Research, 33, 49-64. https://www.jstor.org/stable/170866
Bengtsson, B. E. (1982). Packing rectangular pieces – A heuristic approach. The Computer Journal, 25, 353-357. https://doi.org/10.1093/comjnl/25.3.353
Bennel, J., & Oliveira, J. (2008). The geometry of nesting problems: A tutorial. European Journal of Operational Research, 184, 397-415. https://doi.org/10.1016/j.ejor.2006.11.038
Berkey, J. O., & Wang, P. Y. (1987). Two-dimensional finite bin-packing algorithms. Journal of the Operational Research Society, 38, 423-429. https://doi.org/10.2307/2582731
Berkmanns, J., & Faerber, M. (2008). Laser cutting LASERLINE®. Retrieved from https://www.boconline.co.uk/en/images/laser-cutting_tcm410-39553.pdf
Bertolini, M., Mezzogori, D., & Zammori, F. (2024). Hybrid heuristic for the one-dimensional cutting stock problem with usable leftovers and additional operating constraints. International Journal of Industrial Engineering Computations, 15(1), 149-170. https://doi.org/10.5267/j.ijiec.2023.10.006
Bortfeldt, A., & Jungmann, S. (2012). A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint. Annals of Operations Research, 196, 53-71. https://doi.org/10.1007/s10479-012-1084-7
Brandão, F., & Pedroso, J. P. (2014). Fast pattern-based algorithms for cutting stock. Computers & Operations Research, 48, 69-80. https://doi.org/10.1016/j.cor.2014.03.003
Buchwald, T., & Scheithauer, G. (2016). Upper bounds for heuristic approaches to the strip packing problem. International Transactions in Operational Research, 23, 93-111. https://doi.org/10.1111/itor.12100
Buer, S. V., Stranghagen, J. O., & Chan, F. T. S. (2018). The link between Industry 4.0 and lean manufacturing: Mapping current research and establishing a research agenda. International Journal of Production Research, 56, 2924-2940. https://doi.org/10.1080/00207543.2018.1442945
Burke, E. K., Kendal, G., & Whitwell, G. (2004). A new placement heuristic for the orthogonal stock-cutting problem. Operations Research, 52, 655-671. https://doi.org/10.1287/opre.1040.0109
Bystronic. (2023). BySmart Fiber: Smart access for laser cutting of metal. Retrieved from https://www.bystronic.com/usa/en-us/l/laser-cutting-metal-bysmart-fiber. Accessed September 28, 2024.
Çaidas, U., & Hasçalik, A. (2008). Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics. Optics & Laser Technology, 40, 987-994. https://doi.org/10.1016/j.optlastec.2008.01.004
Chazelle, B. (1983). The bottom-left bin-packing heuristic: An efficient implementation. IEEE Transactions on Computing, 100, 697-707. https://doi.org/10.1109/TC.1983.1676307
Chen, B., Wang, Y., & Yang, S. (2015). A hybrid demon algorithm for the two-dimensional orthogonal strip packing problem. Mathematical Problems in Engineering, 2015, 541931. https://doi.org/10.1155/2015/541931
Chen, W., Zhai, P., Zhu, H., & Zhang, Y. (2014). Hybrid algorithm for the two-dimensional rectangular layer-packing problem. Journal of the Operational Research Society, 65(7), 1068–1077. https://doi.org/10.1057/jors.2013.54
Chernov, N., Stoyan, Y., & Romanova, T. (2010). Mathematical model and efficient algorithms for object packing problem. Computational Geometry, 43, 535–553. https://doi.org/10.1016/j.comgeo.2009.12.003
Cherri, A. C., Arenales, M. N., & Yansse, H. H. (2013). The usable leftover one-dimensional cutting stock problem—a priority-in-use heuristic. International Transactions in Operational Research, 20, 189–199. https://doi.org/10.1111/j.1475-3995.2012.00868.x
Christofides, N., & Whitlock, C. (1977). An algorithm for two-dimensional cutting problems. Operations Research, 25, 30–44. https://www.jstor.org/stable/169545
Coffman, E., Garey, M. R., Johnson, D. S., & Tarjan, R. E. (1980). Performance bounds for level-oriented two-dimensional packing algorithms. SIAM Journal on Computing, 9, 808–826. https://doi.org/10.1137/0209062
Coffman, E. F., & Shor, P. W. (1990). Average-case analysis of cutting and packing in two dimensions. European Journal of Operational Research, 44, 134–144. https://doi.org/10.1016/0377-2217(90)90349-G
Côté, J. F., & Iori, M. (2018). The Meet-in-the-Middle Principle for Cutting and Packing. INFORMS Journal on Computing, 30, 646–661. https://doi.org/10.1287/ijoc.2018.0806
Cui, Y., Yang, L., & Cheng, Q. (2013). Heuristic for the rectangular strip packing problem with rotation of items. Computers & Operations Research, 40, 1094–1099. https://doi.org/10.1016/j.cor.2012.11.020
Cui, Y., Yang, Y., Cheng, X., & Song, P. (2008). A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem. Computers & Operations Research, 35, 1281–1291. https://doi.org/10.1016/j.cor.2006.08.011
Elsheikh, A. H., Shehabeldeen, T. A., Zhou, J., Showaib, E., & Elaziz, M. A. (2021). Prediction of laser cutting parameters for polymethylmethacrylate sheets using random vector functional link network integrated with equilibrium optimizer. Journal of Intelligent Manufacturing, 32, 1377–1388. https://doi.org/10.1007/s10845-020-01617-7
Eswaramoorthi, M., Kathiresan, G. R., Prasa, P. S. S., & Mohanram, P. V. (2011). A survey on lean practices in Indian machine tool industries. The International Journal of Advanced Manufacturing Technology, 52, 1091–1101. https://doi.org/10.1007/s00170-010-2788-y
Fanslau, T., & Bortfeldt, A. (2010). A tree search algorithm for solving the container loading problem. INFORMS Journal on Computing, 22, 222–235. https://doi.org/10.1287/ijoc.1090.0338
Francescatto, M., Neuenfeldt, A., Silva, E., Furtado, J. C., & Bromberger, D. (2023). Impact of minimum distance constraints on sheet metal waste for plasma cutting. PLOS ONE. https://doi.org/10.1371/journal.pone.0292032
Gaustad, G., Krystofik, M., Bustamente, M., & Badami, K. (2018). Circular economy strategies for mitigating critical material supply issues. Resources, Conservation & Recycling, 135, 24–33. https://doi.org/10.1016/j.resconrec.2017.08.002
Ghany, K. A., & Newishy, M. (2005). Cutting of 1.2 mm thick austenitic stainless steel sheet using pulsed and CW Nd laser. Journal of Materials Processing Technology, 168, 438–447. https://doi.org/10.1016/j.jmatprotec.2005.02.251
Gracia, C., Andrés, C., & Gracia, L. (2013). A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company. Journal of Heuristics, 19, 253–273. https://doi.org/10.1007/s10732-011-9187-x
Hifi, M., & Ouafi, R. (1998). A Best-first Branch-and-bound algorithm for orthogonal rectangular packing problems. International Transactions in Operational Research, 5(3), 345–356. https://doi.org/10.1016/S0969-6016(98)00026-4
Hopper, E. (2000). Two-dimensional packing utilizing evolutionary algorithms and other meta-heuristic methods [Ph.D. thesis].
Hopper, E., & Turton, B. (1999). A genetic algorithm for a 2D industrial packing problem. Computers & Industrial Engineering, 37(3), 375–378. https://doi.org/10.1016/S0360-8352(99)00097-2
Hopper, E., & Turton, B. C. H. (2001). Empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research, 128(1), 34–57. https://doi.org/10.1016/S0377-2217(99)00357-4
Imahori, S., & Yagiura, M. (2010). The best-fit heuristic for the rectangular strip packing problem: An efficient implementation and the worst-case approximation ratio. Computers and Operations Research, 37(3), 325–333. https://doi.org/10.1016/j.cor.2009.05.008
Iori, M., de Lima, V. L., Martello, S., Miyazawa, F. K., & Monaci, M. (2021). Exact solution techniques for two-dimensional cutting and packing. European Journal of Operational Research, 289(2), 399–415. https://doi.org/10.1016/j.ejor.2020.06.050
Jasti, N. V. K., & Kodali, R. (2014). Lean production: Literature review and trends. International Journal of Production Research, 53(3), 867–885. https://doi.org/10.1080/00207543.2014.937508
Júnior, A. N., Silva, E., Francescatto, M., Rosa, C. B., & Siluk, J. (2022). The rectangular two-dimensional strip packing problem real-life practical constraints: A bibliometric overview. Computers & Operations Research, 137, 105521. https://doi.org/10.1016/j.cor.2021.105521
Kokten, E. S., & Sel, Ç. (2022). A cutting stock problem in the wood products industry: A two-stage solution approach. International Transactions in Operational Research, 29(3), 879–907. https://doi.org/10.1111/itor.12802
Kos, L., & Duhvonik, J. (2002). Cutting optimization with variable-sized stock and inventory status data. International Journal of Production Research, 40(11), 2289–2301. https://doi.org/10.1080/00207540210128161
Leung, S. C. H., & Zhang, D. (2011). A fast layer-based heuristic for non-guillotine strip packing. Expert Systems with Applications, 38(10), 13032–13042. https://doi.org/10.1016/j.eswa.2011.04.105
Liu, D., & Teng, H. (1999). An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research, 112(3), 413–420. https://doi.org/10.1016/S0377-2217(97)00437-2
Liu, K., Zhang, H., Wang, C., Li, H., Chen, Y., & Chen, Q. (2023). Robust optimization for the two-dimensional strip-packing problem with variable-sized bins. Mathematics, 11(23), 4781. https://doi.org/10.3390/math11234781
Lodi, A., Martello, S., & Vigo, D. (1999). Approximation algorithms for the oriented two-dimensional bin packing problem. European Journal of Operational Research, 112(1), 158–166. https://doi.org/10.1016/S0377-2217(97)00388-3
Madhukar, Y. K., Mullic, S., & Nath, A. K. (2016). An investigation on co-axial water-jet assisted fiber laser cutting of metal sheets. Optics and Lasers in Engineering, 77, 203–218. https://doi.org/10.1016/j.optlaseng.2015.08.003
Martello, S., Monaci, M., & Vigo, D. (2003). An exact approach to the strip-packing problem. INFORMS Journal on Computing, 15(3), 310–319. https://doi.org/10.1287/ijoc.15.3.310.16082
Nascimento, D., Alencastro, V., Quelhas, O., Caiado, R., Garza-Reyes, J., Rocha-Lona, L., & Tortorella, G. (2018). Exploring Industry 4.0 technologies to enable circular economy practices in a manufacturing context: A business model proposal. Journal of Manufacturing Technology Management, 30(3), 607–627. https://doi.org/10.1108/JMTM-03-2018-0071
Na, G.-Y., & Yang, J. (2023). Two-dimensional polygon classification and pairwise clustering for pairing in ship parts nesting. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-023-02196-z
Neuenfeldt, A. J., Francescatto, M., Araújo, O., Disconzi, D., & Stieler, G. (2023). The machining torch movement for the rectangular plasma sheet metal cut. PLoS ONE. https://doi.org/10.1371/journal.pone.0291184
Ntene, N. (2007). An algorithmic approach to the 2D oriented strip packing problem (PhD thesis).
Ntene, N., & Van Vuuren, J.H. (2009). A survey and comparison of guillotine heuristics for the 2D oriented offline strip packing problem. Discrete Optimization, 6, 174–188. https://doi.org/10.1016/j.disopt.2008.11.002
Oliveira, J. F., Neuenfeldt Jr, A., Silva, E., & Carravilla, M. A. (2016). A survey on heuristics for the two-dimensional rectangular strip packing problem. Pesquisa Operacional, 36, 197–226. https://doi.org/10.1590/0101-7438.2016.036.02.0197
Ortmann, F. G., Ntene, N., & Van Vuuren, J. H. (2010). New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems. European Journal of Operational Research, 203, 306–315. https://doi.org/10.1016/j.ejor.2009.07.024
Özcan, E., Kaiz, Z., & Drake, J. H. (2013). Bidirectional best-fit heuristic considering compound placement for two-dimensional orthogonal rectangular strip packing. Expert Systems with Applications, 40, 4035–4043. https://doi.org/10.1016/j.eswa.2013.01.005
Rajaram, N., Sheikh-Ahmad, J., & Cheraghi, S. H. (2003). C2 laser cut quality of 4130 steel. International Journal of Machine Tools & Manufacture, 43, 351–358. https://doi.org/10.1016/S0890-6955(02)00270-5
Silva, E., Oliveira, J. F., & Wäscher, G. (2014). 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems. European Journal of Operational Research, 237, 846–856. https://doi.org/10.1016/j.ejor.2014.02.059
Sweeney, P. E., & Paternoster, E. R. (1992). Cutting and packing problems: A categorized, application-orientated research bibliography. Journal of Operational Research Society, 43, 691–706. https://doi.org/10.2307/2583579
TRUMPF. (2023). 2D laser cutting machines TruLaser 1030 fiber/1040 fiber/1060 fiber. Retrieved from https://www.trumpf.com/en_INT/products/machines-systems/2d-laser-cutting-machines/trulaser-1030-fiber-1040-fiber-1060-fiber/. Accessed September 28, 2024.
Vasilyev, I., Ushakov, A. V., Zhang, D., & Ren, J. (2023). Generalized multiple strip packing problem: Formulations, applications, and solution algorithms. Computers & Industrial Engineering, 178, 109096. https://doi.org/10.1016/j.cie.2023.109096
Vinodh, S., Kumar, S. V., & Vimal, K. E. K. (2012). Implementing lean sigma in an Indian rotary switches manufacturing organization. Production Planning & Control, 25, 288–302. https://doi.org/10.1080/09537287.2012.684726
Wang, P. Y., & Valenzuela, C. L. (2001). Data set generation for rectangular placement problems. European Journal of Operational Research, 134, 378–391. https://doi.org/10.1016/S0377-2217(00)00263-0
Wang, Z., Daofang, C., & Xingyu, M. (2022). Optimization of two-dimensional irregular bin packing problem considering slit distance and free rotation of pieces. International Journal of Industrial Engineering Computations, 13(4), 491–506. https://doi.org/10.5267/j.ijiec.2022.8.001
Wäscher, G., Haußner, H., & Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research, 183, 1109–1130. https://doi.org/10.1016/j.ejor.2005.12.047
Wei, L., Tian, T., Hu, Z., & Lim, A. (2014). A block-based layer building approach for the 2D guillotine strip packing problem. European Journal of Operational Research, 239, 58–69. https://doi.org/10.1016/j.ejor.2014.04.020
Wei, L., Wang, Y., Cheng, H., & Huang, J. (2019). An open space-based heuristic for the 2D strip packing problem with unloading constraints. Applied Mathematical Modelling, 70, 67–81. https://doi.org/10.1016/j.apm.2019.01.022
Xu, J., & Yang, W. (2022). Multi-objective steel plate cutting optimization problem based on real number coding genetic algorithm. Scientific Reports, 12, 22472. https://doi.org/10.1038/s41598-022-27100-2
Yao, S., Zhang, H., Wei, L., & Liu, Q. (2025). An exact approach for the two-dimensional strip packing problem with defects. Computers & Industrial Engineering, 200(110866). https://doi.org/10.1016/j.cie.2025.110866