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A Branch and Bound Algorithm to Minimize Total Weighted Tardiness on a Single Processor

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  • Pascal Babu
  • Laurent Peridy
  • Eric Pinson

Abstract

In this paper, we consider the problem of minimizing the total weighted tardiness of a set of jobs processed on a single processor. First, a lower bound based on a Lagrangian decomposition is presented. The particularity of this decomposition, based on a 0–1 time indexed formulation, is to be sensitive to the domain reduction of jobs which are proposed. A branch and bound strategy including these different components is proposed. The results obtained on problems from the literature can be favourably compared to previously works and seem to prove that a trade-off between a tight lower bound and time consuming in the enumeration process can be a good strategy. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Pascal Babu & Laurent Peridy & Eric Pinson, 2004. "A Branch and Bound Algorithm to Minimize Total Weighted Tardiness on a Single Processor," Annals of Operations Research, Springer, vol. 129(1), pages 33-46, July.
    • Handle: RePEc:spr:annopr:v:129:y:2004:i:1:p:33-46:10.1023/b:anor.0000030680.29037.d0
    DOI: 10.1023/B:ANOR.0000030680.29037.d0
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    Cited by:

    1. Tanaka, Shunji & Araki, Mituhiko, 2008. "A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines," International Journal of Production Economics, Elsevier, vol. 113(1), pages 446-458, May.
    2. Louis-Philippe Bigras & Michel Gamache & Gilles Savard, 2008. "Time-Indexed Formulations and the Total Weighted Tardiness Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 133-142, February.
    3. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2012. "Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one," Annals of Operations Research, Springer, vol. 196(1), pages 247-261, July.
    4. Yunpeng Pan & Zhe Liang, 2017. "Dual relaxations of the time-indexed ILP formulation for min–sum scheduling problems," Annals of Operations Research, Springer, vol. 249(1), pages 197-213, February.

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