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

E G Birgin (), R D Lobato and R Morabito
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E G Birgin: University of São Paulo
R D Lobato: University of São Paulo
R Morabito: Federal University of São Paulo

Journal of the Operational Research Society, 2010, vol. 61, issue 2, 306-320

Abstract: 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.

Keywords: cutting and packing; manufacturer's pallet loading problem; woodpulp stowage problem; non-guillotine cutting pattern; dynamic programming; raster points (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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DOI: 10.1057/jors.2008.141

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