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Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

Author

Listed:
  • Miaomiao Jin

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

  • Xiaoxia Liu

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

  • Wenchang Luo

    (School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China)

Abstract

We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

Suggested Citation

  • Miaomiao Jin & Xiaoxia Liu & Wenchang Luo, 2020. "Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection," Mathematics, MDPI, vol. 8(2), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:258-:d:321211
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    References listed on IDEAS

    as
    1. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    2. Guochuan Zhang & Xiaoqiang Cai & C.‐Y Lee & C.K Wong, 2001. "Minimizing makespan on a single batch processing machine with nonidentical job sizes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 226-240, April.
    3. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    Full references (including those not matched with items on IDEAS)

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