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The single machine serial batch scheduling problem with rejection to minimize total completion time and total rejection cost

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  • Shabtay, Dvir

Abstract

We study a scheduling problem with rejection on a single serial batching machine, where the objectives are to minimize the total completion time and the total rejection cost. We consider four different problem variations. The first is to minimize the sum of the two objectives. The second and the third are to minimize one objective, given an upper bound on the value of the other objective and the last is to find a Pareto-optimal solution for each Pareto-optimal point. We provide a polynomial time procedure to solve the first variation and show that the three other variations are NP-hard. For solving the three NP-hard problems, we construct a pseudo-polynomial time algorithm. Finally, for one of the NP-hard variants of the problem we propose an FPTAS, provided some conditions hold.

Suggested Citation

  • Shabtay, Dvir, 2014. "The single machine serial batch scheduling problem with rejection to minimize total completion time and total rejection cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 64-74.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:64-74
    DOI: 10.1016/j.ejor.2013.08.013
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    References listed on IDEAS

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    1. Dvir Shabtay & Nufar Gaspar & Liron Yedidsion, 2012. "A bicriteria approach to scheduling a single machine with job rejection and positional penalties," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 395-424, May.
    2. Yuan, J. J. & Yang, A. F. & Cheng, T. C. E., 2004. "A note on the single machine serial batching scheduling problem to minimize maximum lateness with identical processing times," European Journal of Operational Research, Elsevier, vol. 158(2), pages 525-528, October.
    3. Mosheiov, Gur & Oron, Daniel, 2008. "A single machine batch scheduling problem with bounded batch size," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1069-1079, June.
    4. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    5. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
    6. Cheng, T. C. Edwin & Janiak, Adam & Kovalyov, Mikhail Y., 2001. "Single machine batch scheduling with resource dependent setup and processing times," European Journal of Operational Research, Elsevier, vol. 135(1), pages 177-183, November.
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    Citations

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    Cited by:

    1. Jinwen Ou, 2020. "Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection," Journal of Scheduling, Springer, vol. 23(5), pages 525-538, October.
    2. Du-Juan Wang & Yunqiang Yin & Mengqi Liu, 2016. "Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3691-3705, June.
    3. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    4. Gur Mosheiov & Vitaly A. Strusevich, 2017. "Determining optimal sizes of bounded batches with rejection via quadratic min‐cost flow," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 217-224, April.
    5. Jun-Qiang Wang & Guo-Qiang Fan & Zhixin Liu, 2020. "Mixed batch scheduling on identical machines," Journal of Scheduling, Springer, vol. 23(4), pages 487-496, August.
    6. Jae-Min Yu & Rong Huang & Dong-Ho Lee, 2017. "Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3266-3282, June.
    7. Juan Zou & Cuixia Miao, 2016. "The single machine serial batch scheduling problems with rejection," Operational Research, Springer, vol. 16(2), pages 211-221, July.
    8. Wenchang Luo & Rylan Chin & Alexander Cai & Guohui Lin & Bing Su & An Zhang, 2022. "A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 690-722, August.
    9. Wu, Wei & Hayashi, Takito & Haruyasu, Kato & Tang, Liang, 2023. "Exact algorithms based on a constrained shortest path model for robust serial-batch and parallel-batch scheduling problems," European Journal of Operational Research, Elsevier, vol. 307(1), pages 82-102.
    10. Baruch Mor, 2019. "Minmax scheduling problems with common due-date and completion time penalty," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 50-71, July.
    11. Wang, Dujuan & Yin, Yunqiang & Cheng, T.C.E., 2018. "Parallel-machine rescheduling with job unavailability and rejection," Omega, Elsevier, vol. 81(C), pages 246-260.
    12. Gur Mosheiov & Assaf Sarig & Vitaly Strusevich, 2020. "Minmax scheduling and due-window assignment with position-dependent processing times and job rejection," 4OR, Springer, vol. 18(4), pages 439-456, December.
    13. Pei, Jun & Liu, Xinbao & Fan, Wenjuan & Pardalos, Panos M. & Lu, Shaojun, 2019. "A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers," Omega, Elsevier, vol. 82(C), pages 55-69.
    14. Xiaofei Liu & Weidong Li & Yaoyu Zhu, 2021. "Single Machine Vector Scheduling with General Penalties," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    15. Xueling Zhong & Zhangming Pan & Dakui Jiang, 2017. "Scheduling with release times and rejection on two parallel machines," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 934-944, April.

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