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Bicriterion parallel-machine scheduling of equal-length jobs to minimize total tardiness and number of tardy jobs

Author

Listed:
  • Jing Zhang

    (Zhengzhou University)

  • Rubing Chen

    (Zhengzhou University)

  • Jinjiang Yuan

    (Zhengzhou University)

  • C. T. Ng

    (The Hong Kong Polytechnic University)

  • T. C. E. Cheng

    (The Hong Kong Polytechnic University)

Abstract

We consider bicriterion scheduling of equal-length jobs on uniform parallel machines to minimize total tardiness and number of tardy jobs. The Pareto-scheduling problem is studied in this paper, which includes the hierarchical-scheduling problem as a subversion. By using the single-machine scheduling with generated completion times model introduced by Zhao and Yuan (J Comb Optim 39:637–661, 2020), we present an $$O(n^2)$$ -time algorithm to solve the Pareto-scheduling problem, and two $$O(n\log n)$$ -time algorithms to solve two hierarchical-scheduling problems, respectively. Our $$O(n\log n)$$ -time algorithms improve the $$O(n^2\log n)$$ -time algorithms given by Sarin and Prakash (J Comb Optim 8:227–240, 2004) to solve two hierarchical-scheduling problems on identical parallel machines.

Suggested Citation

  • Jing Zhang & Rubing Chen & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2025. "Bicriterion parallel-machine scheduling of equal-length jobs to minimize total tardiness and number of tardy jobs," Journal of Combinatorial Optimization, Springer, vol. 50(3), pages 1-15, October.
    • Handle: RePEc:spr:jcomop:v:50:y:2025:i:3:d:10.1007_s10878-025-01353-9
    DOI: 10.1007/s10878-025-01353-9
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