Abstract
This paper presents an exploratory approach to study and identify the main characteristics of the two-dimensional strip packing problem (2D-SPP). A large number of variables was defined to represent the main problem characteristics, aggregated in six groups, established through qualitative knowledge about the context of the problem. Coefficient correlation are used as a quantitative measure to validate the assignment of variables to groups. A principal component analysis (PCA) is used to reduce the dimensions of each group, taking advantage of the relations between variables from the same group. Our analysis indicates that the problem can be reduced to 19 characteristics, retaining most part of the total variance. These characteristics can be used to fit regression models to estimate the strip height necessary to position all items inside the strip.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
J.E. Beasley, An exact two-dimensional non-guillotine cutting tree search procedure. Oper. Res. 33(1), 49–64 (1985)
J.E. Beasley, Algorithms for unconstrained two-dimensional guillotine cutting. J. Oper. Res. Soc. 297–306 (1985)
B.E. Bengtsson, Packing rectangular pieces - a heuristic approach. Comput. J. 25(3), 353–357 (1982)
J.O. Berkey, P.Y. Wang, Two-dimensional finite bin-packing algorithms. J. Oper. Res. Soc. 423–429 (1987)
A. Bortfeldt, A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces. Eur. J. Oper. Res. 172(3), 814–837 (2006)
A. Bortfeldt, H. Gehring, A hybrid genetic algorithm for the container loading problem. Eur. J. Oper. Res. 131(1), 143–161 (2001)
E.K. Burke, G. Kendall, G. Whitwell, A new placement heuristic for the orthogonal stock-cutting problem. Oper. Res. 52(4), 655–671 (2004)
N. Christofides, C. Whitlock, An algorithm for two-dimensional cutting problems. Oper. Res. 25(1), 30–44 (1977)
E.P. Ferreira, J.F. Oliveira, A note on Fekete and Schepers’ algorithm for the non-guillotinable two-dimensional packing problem (Technical report, FEUP, 2005)
N.G. Hall, M.E. Posner, Generating experimental data for computational testing with machine scheduling applications. Oper. Res. 49(6), 854–865 (2001)
E. Hopper, B.C.H. Turton, An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem. Eur. J. Oper. Res. 128, 34–57 (2001)
E. Hopper, Two-dimensional packing utilising evolutionary algorithms and other meta-heuristic methods. PhD thesis, University of Wales, Cardiff, 2000
S. Imahori, M. Yagiura, The best-fit heuristic for the rectangular strip packing problem: An efficient implementation and the worst-case approximation ratio. Comput. Oper. Res. 37(2), 325–333 (2010)
S.C.H. Leung, D. Zhang, A fast layer-based heuristic for non-guillotine strip packing. Expert Syst. Appl. 38(10), 13032–13042 (2011)
S.C.H Leung, D. Zhang, K.M. Sim, A two-stage intelligent search algorithm for the two-dimensional strip packing problem. Eur. J. Oper. Res. 215(1):57–69 (2011)
E. López-Camacho, H. Terashima-Marín, G. Ochoa, S.E. Conant-Pablos, Understanding the structure of bin packing problems through principal component analysis. Int. J. Prod. Econ. 145(2), 488–499 (2013)
E. López–Camacho, H. Terashima–Marin, P. Ross, G. Ochoa, A unified hyper-heuristic framework for solving bin packing problems. Expert Syst. Appl. 41(15), 6876–6889 (2014)
S. Martello, D. Vigo, Exact solution of the two-dimensional finite bin packing problem. Manag. Sci. 44(3), 388–399 (1998)
J.F. Oliveira, A.N. Júnior, E. Silva, M.A. Carravilla, A survey on heuristics for the two-dimensional rectangular strip packing problem. Pesqui. Oper. 36(2):197–226 (2016)
E. Silva, J.F. Oliveira, G. Wäscher, 2DCPackGen: a problem generator for two-dimensional rectangular cutting and packing problems. Eur. J. Oper. Res. 237(3), 846–856 (2014)
K. Smith–Miles, L. Lopes, Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)
P.Y. Wang, C.L. Valenzela, Data set generation for rectangular placement problems. Eur. J. Oper. Res. 134(2), 378–391 (2001)
G. Wäscher, H. Haußner, H. Schumann, An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007)
Acknowledgements
The second author was supported by FCT – Fundação para a Ciência e a Tecnologia within the grant SFRH/BPD/98981/2013. The research was partially supported by ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia as part of project “UID/EEA/50014/2013”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Neuenfeldt Júnior, A., Silva, E., Miguel Gomes, A., Oliveira, J.F. (2018). The Two-Dimensional Strip Packing Problem: What Matters?. In: Vaz, A., Almeida, J., Oliveira, J., Pinto, A. (eds) Operational Research. APDIO 2017. Springer Proceedings in Mathematics & Statistics, vol 223. Springer, Cham. https://doi.org/10.1007/978-3-319-71583-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-71583-4_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71582-7
Online ISBN: 978-3-319-71583-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)