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Worst‐case analysis of local search heuristics for the one‐machine total tardiness problem

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  • Shiwei Chang
  • Hirofumi Matsuo
  • Guochun Tang

Abstract

In this article the worst‐case performance of four local search heuristics for the total tardiness problem is investigated. Since the denominator of the error ratio, which is the optimal objective value, may become zero, the derivation of the worst‐case relative error requires a careful mathematical treatment. After necessary definitions and notations are introduced, the worst‐case relative errors of two heuristics are shown to be infinite for a given number of jobs, while those of the other two are shown to be finite.

Suggested Citation

  • Shiwei Chang & Hirofumi Matsuo & Guochun Tang, 1990. "Worst‐case analysis of local search heuristics for the one‐machine total tardiness problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(1), pages 111-121, February.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:1:p:111-121
    DOI: 10.1002/1520-6750(199002)37:13.0.CO;2-V
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    References listed on IDEAS

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    1. Chris N. Potts & Luk N. Van Wassenhove, 1985. "A Branch and Bound Algorithm for the Total Weighted Tardiness Problem," Operations Research, INFORMS, vol. 33(2), pages 363-377, April.
    2. Kenneth R. Baker & James B. Martin, 1974. "An experimental comparison of solution algorithms for the single‐machine tardiness problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 187-199, March.
    3. Linus Schrage & Kenneth R. Baker, 1978. "Dynamic Programming Solution of Sequencing Problems with Precedence Constraints," Operations Research, INFORMS, vol. 26(3), pages 444-449, June.
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    Cited by:

    1. Koulamas, Christos, 2010. "The single-machine total tardiness scheduling problem: Review and extensions," European Journal of Operational Research, Elsevier, vol. 202(1), pages 1-7, April.
    2. Koulamas, Christos & Kyparisis, George J., 2019. "New results for single-machine scheduling with past-sequence-dependent setup times and due date-related objectives," European Journal of Operational Research, Elsevier, vol. 278(1), pages 149-159.

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