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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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