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

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  • Sergey Kovalev

Abstract

Gafarov et al. (Ann Oper Res 196(1):247–261, 2012 ) have recently presented an $$O(n^2)$$ O ( n 2 ) time dynamic programming algorithm for a single machine scheduling problem to maximize the total job tardiness. We reduce this problem in $$O(n\log n)$$ 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 $$O(n^2)$$ O ( n 2 ) time dynamic programming algorithm is known in the literature. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Sergey Kovalev, 2015. "Maximizing total tardiness on a single machine in $$O(n^2)$$ O ( n 2 ) time via a reduction to half-product minimization," Annals of Operations Research, Springer, vol. 235(1), pages 815-819, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:815-819:10.1007/s10479-015-2023-1
    DOI: 10.1007/s10479-015-2023-1
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    References listed on IDEAS

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    1. Kellerer, Hans & Strusevich, Vitaly, 2013. "Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product," European Journal of Operational Research, Elsevier, vol. 228(1), pages 24-32.
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    6. Xu, Zhou, 2012. "A strongly polynomial FPTAS for the symmetric quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 377-381.
    7. T. Badics & E. Boros, 1998. "Minimization of Half-Products," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 649-660, August.
    8. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2013. "Single machine total tardiness maximization problems: complexity and algorithms," Annals of Operations Research, Springer, vol. 207(1), pages 121-136, August.
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