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Grids for cutting and packing problems: a study in the 2D knapsack problem

Jéssica Gabriela Almeida Cunha (), Vinícius Loti de Lima () and Thiago Alves Queiroz ()
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Jéssica Gabriela Almeida Cunha: Federal University of Goiás - Campus Catalão
Vinícius Loti de Lima: Federal University of Goiás - Campus Catalão
Thiago Alves Queiroz: Federal University of Goiás - Campus Catalão

4OR, 2020, vol. 18, issue 3, No 2, 293-339

Abstract: Abstract Different grids of points to solve cutting and packing problems with rectangular shaped items are discussed in this work. The grids are the canonical dissections (also known as normal patterns), useful numbers, reduced raster points, regular normal patterns, and meet-in-the-middle patterns. Theoretical results involving the size and subset relations among the grids are proposed, besides practical procedures to reduce the size. Computational experiments are performed in which the two-dimensional (2D) knapsack problem is solved with an integer linear programming model. The results show the impact on the grids before and after applying the reduction procedures, concluding that the reduced raster points and meet-in-the-middle patterns are generally the grids with the smallest number of points.

Keywords: Grid of points; Reduction procedures; Canonical dissections; Reduced raster points; Meet-in-the-middle patterns; Two-dimensional knapsack problem; 90C27 Combinatorial optimization; 52C17 Packing and covering in n dimensions; 97M40 Operations research; economics (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10288-019-00419-9

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