Block rearranging elements within matrix columns to minimize the variability of the row sums

K.M.R. Boudt, Edgars Jakobsons, Steven Vanduffel

Research output: Contribution to JournalArticleAcademicpeer-review

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.

LanguageEnglish
Pages31–50
Number of pages20
Journal4OR
Volume16
DOIs
StatePublished - 2018

Fingerprint

Equalization
Rearrangement
Minimise
Partitioning
Crew Scheduling
Assembly Line
Operations research
Operations Research
Greedy Algorithm
Scheduling Problem
Optimality
Permutation
Scheduling
Heuristics
Necessary Conditions
Greedy algorithm
Assembly line

Keywords

  • Assembly line crew scheduling
  • Greedy algorithm
  • k-Partitioning
  • Karmarkar–Karp differencing algorithm
  • Rearrangements

Cite this

Boudt, K.M.R. ; Jakobsons, Edgars ; Vanduffel, Steven. / Block rearranging elements within matrix columns to minimize the variability of the row sums. In: 4OR. 2018 ; Vol. 16. pp. 31–50
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Block rearranging elements within matrix columns to minimize the variability of the row sums. / Boudt, K.M.R.; Jakobsons, Edgars; Vanduffel, Steven.

In: 4OR, Vol. 16, 2018, p. 31–50.

Research output: Contribution to JournalArticleAcademicpeer-review

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AU - Jakobsons,Edgars

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