An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

Author Birgin, E. G. Google Scholar
Lobato, R. D. Google Scholar
Morabito, R. Autor UNIFESP Google Scholar
Institution Universidade de São Paulo (USP)
Universidade Federal de São Paulo (UNIFESP)
Abstract In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. the combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. the computer implementation and the data sets are available for benchmarking purposes. Journal of the Operational Research Society (2010) 61, 306-320. doi: 10.1057/jors.2008.141 Published online 4 February 2009
Keywords cutting and packing
manufacturer's pallet loading problem
woodpulp stowage problem
non-guillotine cutting pattern
dynamic programming
raster points
Language English
Sponsor PRONEX-Optimization
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Grant number PRONEX-Optimization: E-26/171.510/2006-APQ1
FAPESP: 2006/53768-0
FAPESP: 2006/03496-3
FAPESP: 2005/57984-6
CNPq: PROSUL 490333/2004-4
CNPq: 522973/1995-4
Date 2010-02-01
Published in Journal of the Operational Research Society. Basingstoke: Palgrave Macmillan Ltd, v. 61, n. 2, p. 306-320, 2010.
ISSN 0160-5682 (Sherpa/Romeo, impact factor)
Publisher Palgrave Macmillan Ltd
Extent 306-320
Access rights Closed access
Type Article
Web of Science ID WOS:000273247600013

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