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Rescheduling to Minimize the Maximum Lateness Under the Sequence Disruptions of Original Jobs

Author

Listed:
  • Qiulan Zhao

    (Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, P. R. China)

  • Jinjiang Yuan

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China)

Abstract

We introduce and study the rescheduling on a single machine to minimize the maximum lateness under the sequence disruptions of original jobs. In the problem, each original job Jj has a constraint disruption on its sequence respect to an original optimal schedule π, i.e., Dj(π) ≤ kj. That is, if Jj is the xth job in π, then it is required that the position index y of Jj in a schedule for all jobs satisfies |y − x|≤ kj. By introducing the positive sequence disruption Dj+(π) and the negative sequence disruption Dj−(π), three problems are considered in this paper: problem (P1) is 1|Dj(π) ≤ kj|Lmax, problem (P2) is 1|Dj+(π) ≤ k j|Lmax, and problem (P3) is 1|Dj+(π) ≤ k j,Dj−(π) = 0|Lmax. We show that the three problems are equivalent and can be solved in O(nlog n) time. Then we study an extension of problem (P2): 1|prec,σ−1(j) ≤ k j|fmax. We show that the extended problem can be solved in O(n2) time.

Suggested Citation

  • Qiulan Zhao & Jinjiang Yuan, 2017. "Rescheduling to Minimize the Maximum Lateness Under the Sequence Disruptions of Original Jobs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-12, October.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:05:n:s0217595917500245
    DOI: 10.1142/S0217595917500245
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    References listed on IDEAS

    as
    1. Jinjiang Yuan & Yundong Mu & Lingfa Lu & Wenhua Li, 2007. "Rescheduling With Release Dates To Minimize Total Sequence Disruption Under A Limit On The Makespan," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(06), pages 789-796.
    2. Nicholas G. Hall & Chris N. Potts, 2010. "Rescheduling for Job Unavailability," Operations Research, INFORMS, vol. 58(3), pages 746-755, June.
    3. Nicholas G. Hall & Zhixin Liu & Chris N. Potts, 2007. "Rescheduling for Multiple New Orders," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 633-645, November.
    4. Hamsa Balakrishnan & Bala G. Chandran, 2010. "Algorithms for Scheduling Runway Operations Under Constrained Position Shifting," Operations Research, INFORMS, vol. 58(6), pages 1650-1665, December.
    5. Aytug, Haldun & Lawley, Mark A. & McKay, Kenneth & Mohan, Shantha & Uzsoy, Reha, 2005. "Executing production schedules in the face of uncertainties: A review and some future directions," European Journal of Operational Research, Elsevier, vol. 161(1), pages 86-110, February.
    6. Yuan, Jinjiang & Mu, Yundong, 2007. "Rescheduling with release dates to minimize makespan under a limit on the maximum sequence disruption," European Journal of Operational Research, Elsevier, vol. 182(2), pages 936-944, October.
    7. Nicholas G. Hall & Chris N. Potts, 2004. "Rescheduling for New Orders," Operations Research, INFORMS, vol. 52(3), pages 440-453, June.
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    Cited by:

    1. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.

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