Economics at your fingertips  

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 ()
Additional contact information
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
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
https://www.springer ... ch/journal/10288/PSE

DOI: 10.1007/s10288-019-00419-9

Access Statistics for this article

4OR is currently edited by Yves Crama, Michel Grabisch and Silvano Martello

More articles in 4OR from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

Page updated 2020-10-24
Handle: RePEc:spr:aqjoor:v:18:y:2020:i:3:d:10.1007_s10288-019-00419-9