Block rearranging elements within matrix columns to minimize the variability of the row sums
Edgars Jakobsons () and
Steven Vanduffel ()
Additional contact information
Edgars Jakobsons: ETH Zürich
Steven Vanduffel: Vrije Universiteit Brussel (VUB)
4OR, 2018, vol. 16, issue 1, 31-50
Abstract Several problems in operations research, such as the assembly line crew scheduling problem and the k-partitioning problem can be cast as the problem of finding the intra-column rearrangement (permutation) of a matrix such that the row sums show minimum variability. A necessary condition for optimality of the rearranged matrix is that for every block containing one or more columns it must hold that its row sums are oppositely ordered to the row sums of the remaining columns. We propose the block rearrangement algorithm with variance equalization (BRAVE) as a suitable method to achieve this situation. It uses a carefully motivated heuristic—based on an idea of variance equalization—to find optimal blocks of columns and rearranges them. When applied to the number partitioning problem, we show that BRAVE outperforms the well-known greedy algorithm and the Karmarkar–Karp differencing algorithm.
Keywords: Assembly line crew scheduling; Greedy algorithm; Rearrangements; k-Partitioning; Karmarkar–Karp differencing algorithm; 90B35; 90B90; 90C27; 97M40; 90C59 (search for similar items in EconPapers)
References: Add references at CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s10288-017-0344-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:aqjoor:v:16:y:2018:i:1:d:10.1007_s10288-017-0344-4
Ordering information: This journal article can be ordered from
https://www.springer ... ch/journal/10288/PSE
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 ().