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Maximizing total tardiness on a single machine in \(O(n^2)\) time via a reduction to half-product minimization

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Abstract

Gafarov et al. (Ann Oper Res 196(1):247–261, 2012) have recently presented an \(O(n^2)\) time dynamic programming algorithm for a single machine scheduling problem to maximize the total job tardiness. We reduce this problem in \(O(n\log n)\) time to a problem of unconstrained minimization of a function of 0–1 variables, called half-product, for which a simple \(O(n^2)\) time dynamic programming algorithm is known in the literature.

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Authors and Affiliations

  1. INSEEC Business School, ECE Lyon, 25 rue de l’Université, 69007 , Lyon, France

    Sergey Kovalev

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  1. Sergey Kovalev
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Correspondence to Sergey Kovalev.

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Kovalev, S. Maximizing total tardiness on a single machine in \(O(n^2)\) time via a reduction to half-product minimization. Ann Oper Res 235, 815–819 (2015). https://doi.org/10.1007/s10479-015-2023-1

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  • DOI: https://doi.org/10.1007/s10479-015-2023-1

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