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Single Machine Scheduling with Deadlines to Minimize the Weighted Number of Tardy Jobs

Author

Listed:
  • A. M. A. Hariri

    (Department of Statistics, King Abdul-Aziz University, Jeddah, Saudi Arabia)

  • C. N. Potts

    (Faculty of Mathematical Studies, University of Southamption, United Kingdom)

Abstract

This paper considers as single machine scheduling problem in which jobs have due dates and deadlines. A job may be completed after its due date, but not after its deadline, in which case it is tardy. A branch and bound algorithm is proposed to find a schedule which minimizes the weighted number of tardy jobs. It uses lower bounds which are derived using the dynamic programming state-space relaxation method. Computational experience with test problems having up to 300 jobs indicates that the lower bounds are extremely effective in restricting the size of the branch and bound search tree.

Suggested Citation

  • A. M. A. Hariri & C. N. Potts, 1994. "Single Machine Scheduling with Deadlines to Minimize the Weighted Number of Tardy Jobs," Management Science, INFORMS, vol. 40(12), pages 1712-1719, December.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:12:p:1712-1719
    DOI: 10.1287/mnsc.40.12.1712
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    Citations

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    Cited by:

    1. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    2. Hejl, Lukáš & Šůcha, Přemysl & Novák, Antonín & Hanzálek, Zdeněk, 2022. "Minimizing the weighted number of tardy jobs on a single machine: Strongly correlated instances," European Journal of Operational Research, Elsevier, vol. 298(2), pages 413-424.
    3. Gowrishankar, K. & Rajendran, Chandrasekharan & Srinivasan, G., 2001. "Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date," European Journal of Operational Research, Elsevier, vol. 132(3), pages 643-665, August.
    4. Haiyan Wang & Chung‐Yee Lee, 2005. "Production and transport logistics scheduling with two transport mode choices," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 796-809, December.
    5. Koulamas, Christos & Kyparisis, George J., 2001. "Single machine scheduling with release times, deadlines and tardiness objectives," European Journal of Operational Research, Elsevier, vol. 133(2), pages 447-453, January.
    6. Jinjiang Yuan, 2017. "Unary NP-hardness of minimizing the number of tardy jobs with deadlines," Journal of Scheduling, Springer, vol. 20(2), pages 211-218, April.

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