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Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance

Author

Listed:
  • Jing Fan

    (Shanghai Polytechnic University)

  • Hui Shi

    (Shanghai Jiaotong University)

Abstract

We consider the problem of scheduling a set of jobs with different processing times and sizes on a single bounded parallel-batch machine with periodic maintenance. Because the machine is in batch-processing model and the capacity is fixed, several jobs can be processed simultaneously in a batch provided that the total size of the jobs in the batch doesn’t exceed the machine capacity. And the processing time of a batch is the largest processing time of the jobs contained in the batch. Meanwhile, the production of each batch is non-resumable, that is, if a batch cannot be completed processing before some maintenance, that batch needs to be processed anew once the machine returns available. Our goal is to minimize the makespan. We first consider two special cases where the jobs have the same sizes or the same processing times, both of which are strongly NP-hard. We present two different approximation algorithms for them and show that these two algorithms have the same tight worst-case ratio of 2. We then consider the general case where the jobs have the arbitrary processing times and arbitrary sizes, for which we propose a 17/5-approximation algorithm.

Suggested Citation

  • Jing Fan & Hui Shi, 2022. "Non-resumable scheduling on a single bounded parallel-batch machine with periodic maintenance," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1645-1654, July.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:5:d:10.1007_s10878-021-00715-3
    DOI: 10.1007/s10878-021-00715-3
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    References listed on IDEAS

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    1. Guochuan Zhang & Xiaoqiang Cai & C.‐Y Lee & C.K Wong, 2001. "Minimizing makespan on a single batch processing machine with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 226-240, April.
    2. Gyorgy Dosa & Zhiyi Tan & Zsolt Tuza & Yujie Yan & Cecília Sik Lányi, 2014. "Improved bounds for batch scheduling with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 351-358, August.
    3. Jing Fan & Xiwen Lu, 2015. "Supply chain scheduling problem in the hospital with periodic working time on a single machine," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 892-905, November.
    4. Wenhua Li & Xing Chai, 2019. "The medical laboratory scheduling for weighted flow-time," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 83-94, January.
    5. B.‐Y. Cheng & J.Y.‐T. Leung & K. Li & S.‐L. Yang, 2015. "Single batch machine scheduling with deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 470-482, September.
    Full references (including those not matched with items on IDEAS)

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