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

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

*Corresponding author for this work

    Research output: Contribution to JournalArticleAcademicpeer-review

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    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.

    Original languageEnglish
    Pages (from-to)31–50
    Number of pages20
    Journal4OR
    Volume16
    Issue number1
    Early online date2 Mar 2017
    DOIs
    Publication statusPublished - Mar 2018

    Keywords

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

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