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Single-Machine Rescheduling with Rejection and an Operator No-Availability Period

Author

Listed:
  • Guanghua Wu

    (Center for Mathematics and Physics, Weifang University of Science and Technology, Weifang 262700, China)

  • Hongli Zhu

    (School of Management, Qufu Normal University, Rizhao 276826, China)

Abstract

In this paper, we investigate a rescheduling problem with rejection and an operator non-availability period on a single machine. An optimal original schedule with the objective of minimizing the total weighted completion time has been made in a deterministic production scheduling system without an unavailable interval. However, prior to the start of formal job processing, a time interval becomes unavailable due to the operator. No jobs can start or complete in the interval; nonetheless, a job that begins prior to this interval and finishes afterward is possible (if there is such a job, we call it a crossover job). In order to deal with the operator non-availability period, job rejection is allowed. Each job is either accepted for processing or rejected by paying a rejection cost. The planned original schedule is required to be rescheduled. The objective is to minimize the total weighted completion time of the accepted jobs plus the total penalty of the rejected jobs plus the weighted maximum tardiness penalty between the original schedule and the new reschedule. We present a pseudo-polynomial time dynamic programming exact algorithm and subsequently develop it into a fully polynomial time approximation scheme.

Suggested Citation

  • Guanghua Wu & Hongli Zhu, 2024. "Single-Machine Rescheduling with Rejection and an Operator No-Availability Period," Mathematics, MDPI, vol. 12(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3678-:d:1528127
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    References listed on IDEAS

    as
    1. Wenchang Luo & Taibo Luo & Randy Goebel & Guohui Lin, 2018. "Rescheduling due to machine disruption to minimize the total weighted completion time," Journal of Scheduling, Springer, vol. 21(5), pages 565-578, October.
    2. Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
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    8. Wenchang Luo & Rylan Chin & Alexander Cai & Guohui Lin & Bing Su & An Zhang, 2022. "A tardiness-augmented approximation scheme for rejection-allowed multiprocessor rescheduling," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 690-722, August.
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