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Scheduling with step learning and job rejection

Author

Listed:
  • Jiaxin Song

    (Qufu Normal University
    Nanjing University of Information Science and Technology)

  • Cuixia Miao

    (Qufu Normal University)

  • Fanyu Kong

    (Qufu Normal University)

Abstract

This paper focuses on job scheduling with step learning and job rejection. The step learning model aims to reduce the processing time for jobs starting after a specific learning date. Our objective is to minimize the sum of the maximum completion time of accepted jobs and the total rejection penalty of rejected jobs. We examine special cases of processing times for both single-machine and parallel-machine scenarios. For the former, we design a pseudo-polynomial time algorithm, a 2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) based on data rounding. For the latter, we present a fully polynomial-time approximation scheme achieved by trimming the state space. Additionally, for the general case of the single-machine problem, we propose a pseudo-polynomial time algorithm.

Suggested Citation

  • Jiaxin Song & Cuixia Miao & Fanyu Kong, 2025. "Scheduling with step learning and job rejection," Operational Research, Springer, vol. 25(1), pages 1-18, March.
    • Handle: RePEc:spr:operea:v:25:y:2025:i:1:d:10.1007_s12351-024-00887-w
    DOI: 10.1007/s12351-024-00887-w
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