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An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown

Author

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  • Ji Tian

    (China University of Mining and Technology)

  • Yan Zhou

    (China University of Mining and Technology)

  • Ruyan Fu

    (China University of Mining and Technology)

Abstract

We consider a semi-online scheduling problem on a single machine with an unexpected breakdown period. In the problem, each job has a processing time and a subsequent delivery time. All these data are known in the beginning. The scheduler has to determine a sequence S of these jobs for processing. After S is given, a machine unavailability period may occur where its starting time and length are not known in advance. The objective is to minimize the time by which all jobs are delivered. We present an online algorithm with a competitive ratio of $$\frac{\sqrt{5}+1}{2}\approx 1.618$$5+12≈1.618, which improves the previously known algorithm with $$\frac{2+\sqrt{2}}{2}\approx 1.707$$2+22≈1.707-competitive.

Suggested Citation

  • Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:1:d:10.1007_s10878-020-00572-6
    DOI: 10.1007/s10878-020-00572-6
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    References listed on IDEAS

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    1. Liu, Ming & Chu, Chengbin & Xu, Yinfeng & Zheng, Feifeng, 2010. "An optimal online algorithm for single machine scheduling with bounded delivery times," European Journal of Operational Research, Elsevier, vol. 201(3), pages 693-700, March.
    2. Qijia Liu & Long Wan & Lijun Wei, 2015. "Online Scheduling on a Single Machine with Grouped Processing Times," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, April.
    3. Peihai Liu & Xiwen Lu, 2015. "Online unbounded batch scheduling on parallel machines with delivery times," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 228-236, January.
    4. Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
    5. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    6. Xinrong Lu & Zhaohui Liu, 2015. "Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-31.
    7. Jinjiang Yuan & Lei Shi & Jinwen Ou, 2008. "Single Machine Scheduling With Forbidden Intervals And Job Delivery Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 317-325.
    8. Peihai Liu & Xiwen Lu, 2015. "Online scheduling on two parallel machines with release dates and delivery times," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 347-359, August.
    9. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    10. Xiao Min & Jing Liu & Yanxia Dong & Ming Jiang, 2015. "Online Preemptive Hierarchical Scheduling on Two Uniform Machines with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-15.
    11. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
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    Cited by:

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