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

被引：13
|
作者：
de Almeida Cunha, Jessica Gabriela [1 ]
De Lima, Vinicius Loti [1 ]
de Queiroz, Thiago Alves [1 ]
机构：
[1] Univ Fed Goias, Inst Math & Technol, Campus Catalao, BR-75704020 Catalao, Go, Brazil
来源：
4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH | 2020年 / 18卷 / 03期
关键词：
Grid of points; Reduction procedures; Canonical dissections; Reduced raster points; Meet-in-the-middle patterns; Two-dimensional knapsack problem; EXACT ALGORITHM; STOCK;
D O I：
10.1007/s10288-019-00419-9
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
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.
引用
收藏
页码：293 / 339
页数：47
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