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Approximation algorithms for batch scheduling with processing set restrictions

Author

Listed:
  • Xing Chai

    (Zhengzhou University
    Henan University of Technology)

  • Wenhua Li

    (Zhengzhou University)

  • C. T. Ng

    (The Hong Kong Polytechnic University)

  • T. C. E. Cheng

    (The Hong Kong Polytechnic University)

Abstract

We consider batch scheduling on m machines to minimize the makespan. Each job has a given set of machines to be assigned. Each machine can process several jobs simultaneously as a batch, and the machines may have different batch capacities. We study two models: (i) scheduling on equal-speed batch machines under a nested processing set restriction, where the machines have the same processing speed, and (ii) scheduling on uniform batch machines under a tree-hierarchical processing set restriction, where the machines have different processing speeds. For both models we design polynomial-time approximation algorithms to solve them. The algorithms have a worst-case ratio of 2 for non-identical batch capacities and a worst-case ratio of $$2-1/m$$ 2 - 1 / m for identical batch capacities.

Suggested Citation

  • Xing Chai & Wenhua Li & C. T. Ng & T. C. E. Cheng, 2023. "Approximation algorithms for batch scheduling with processing set restrictions," Journal of Scheduling, Springer, vol. 26(6), pages 523-533, December.
    • Handle: RePEc:spr:jsched:v:26:y:2023:i:6:d:10.1007_s10951-022-00720-2
    DOI: 10.1007/s10951-022-00720-2
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    References listed on IDEAS

    as
    1. Leung, Joseph Y.-T. & Li, Chung-Lun, 2016. "Scheduling with processing set restrictions: A literature update," International Journal of Production Economics, Elsevier, vol. 175(C), pages 1-11.
    2. Chi To Ng & T. C. E. Cheng & Eugene Levner & Boris Kriheli, 2021. "Optimal bi-criterion planning of rescue and evacuation operations for marine accidents using an iterative scheduling algorithm," Annals of Operations Research, Springer, vol. 296(1), pages 407-420, January.
    3. Li, Shuguang, 2017. "Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan," European Journal of Operational Research, Elsevier, vol. 260(1), pages 12-20.
    4. Epstein, Leah & Levin, Asaf, 2011. "Scheduling with processing set restrictions: PTAS results for several variants," International Journal of Production Economics, Elsevier, vol. 133(2), pages 586-595, October.
    5. Leung, Joseph Y-T. & Ng, C.T., 2017. "Fast approximation algorithms for uniform machine scheduling with processing set restrictions," European Journal of Operational Research, Elsevier, vol. 260(2), pages 507-513.
    6. Chung Keung Poon & Wenci Yu, 2005. "On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 167-186, March.
    7. Chung Poon & Wenci Yu, 2005. "A Flexible On-line Scheduling Algorithm for Batch Machine with Infinite Capacity," Annals of Operations Research, Springer, vol. 133(1), pages 175-181, January.
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