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New approximation algorithms for machine scheduling with rejection on single and parallel machine

Author

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  • Peihai Liu

    (East China University of Science and Technology)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

In this paper we consider three machine scheduling problems with the special feature that jobs may be rejected at a certain penalty. There are n jobs which are characterized by a release date, a processing time and a penalty. Each job is either accepted and then processed by one machine, or rejected and then a rejection penalty is paid. The objective is to minimize the maximum completion time of all accepted job plus the total penalties of all rejected jobs. When jobs have identical release dates, we present a ( $$\frac{3}{2}-\frac{1}{2m}$$ 3 2 - 1 2 m )-approximation algorithm for the parallel machine problem. When jobs have general release dates, we propose a $$\frac{4}{3}$$ 4 3 -approximation algorithm for the single machine problem and a ( $$1+\max \{0.618,1-\frac{1}{m}\}$$ 1 + max { 0.618 , 1 - 1 m } )-approximation algorithm for the parallel machine problem, respectively.

Suggested Citation

  • Peihai Liu & Xiwen Lu, 2020. "New approximation algorithms for machine scheduling with rejection on single and parallel machine," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 929-952, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00642-9
    DOI: 10.1007/s10878-020-00642-9
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    References listed on IDEAS

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    1. Cheng He & Joseph Y.-T. Leung & Kangbok Lee & Michael L. Pinedo, 2016. "Improved algorithms for single machine scheduling with release dates and rejections," 4OR, Springer, vol. 14(1), pages 41-55, March.
    2. Xueling Zhong & Jinwen Ou, 2017. "Improved approximation algorithms for parallel machine scheduling with release dates and job rejection," 4OR, Springer, vol. 15(4), pages 387-406, December.
    3. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.
    4. Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    5. George Steiner & Rui Zhang, 2011. "Revised Delivery-Time Quotation in Scheduling with Tardiness Penalties," Operations Research, INFORMS, vol. 59(6), pages 1504-1511, December.
    6. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    7. Lu, Lingfa & Ng, C.T. & Zhang, Liqi, 2011. "Optimal algorithms for single-machine scheduling with rejection to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 130(2), pages 153-158, April.
    8. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    9. 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.
    10. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
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    Cited by:

    1. Lingfa Lu & Liqi Zhang, 2023. "Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-17, August.
    2. Ou, Jinwen & Lu, Lingfa & Zhong, Xueling, 2023. "Parallel-batch scheduling with rejection: Structural properties and approximation algorithms," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1017-1032.

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