Abstract
Within this chapter we address those two- and higher-dimensional cutting and packing problems where the guillotine cutting condition has to be regarded. That means, given a pattern then the desired products can be obtained by a sequence of guillotine cuts. We will consider knapsack-type problems as well as cutting stock problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R.R. Amossen, D. Pisinger, Multi-dimensional bin packing problems with guillotine constraints. Comput. Oper. Res. 37, 1999–2006 (2010)
G.F. Cintra, F.K. Miyazawa, Y. Wakabayashi, E.C. Xavier, Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation. Eur. J. Oper. Res. 191, 61–85 (2008)
T.A. de Queiroz, F.K. Miyazawa, Y. Wakabayashi, E.C. Xavier, Algorithms for 3d guillotine cutting problems: unbounded knapsack, cutting stock and strip packing. Comput. Oper. Res. 39, 200–212 (2012)
H. Dyckhoff, A new linear approach to the cutting stock problem. Oper. Res. 29(6), 1092–1104 (1981)
F. Furini, E. Malaguti, R.M. Durán, A. Persiani, P. Toth, A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size. Eur. J. Oper. Res. 218(1), 251–260 (2012)
G. Galambos, A. van Vliet, Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms. Computing 52, 281–297 (1994)
P.C. Gilmore, R.E. Gomory, Multistage cutting stock problems of two and more dimensions. Oper. Res. 13, 94–120 (1965)
A. Lodi, M. Monaci, Integer linear programming models for 2-staged two-dimensional knapsack problems. Math. Program. Ser. B 94, 257–278 (2003)
J. Puchinger, G.R. Raidl, Models and algorithms for three-stage two-dimensional bin packing. Eur. J. Oper. Res. 183, 1304–1327 (2007)
G. Scheithauer, On the MAXGAP problem for cutting stock problems. J. Inf. Process. Cybern. 30, 111–117 (1994)
E. Silva, F. Alvelos, J.M.V. de Carvalho, An integer programming model for two- and three-stage two-dimensional cutting stock problems. Eur. J. Oper. Res. 205, 699–708 (2010)
P.Y. Wang, Two algorithms for constrained two-dimensional cutting stock problems. Oper. Res. 31, 573–586 (1983)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Scheithauer, G. (2018). Optimal Guillotine Cutting. In: Introduction to Cutting and Packing Optimization. International Series in Operations Research & Management Science, vol 263. Springer, Cham. https://doi.org/10.1007/978-3-319-64403-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-64403-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64402-8
Online ISBN: 978-3-319-64403-5
eBook Packages: Business and ManagementBusiness and Management (R0)