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Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions

Author

Listed:
  • C-C Wu

    (Feng Chia University, Taichung, Taiwan)

  • Y Yin

    (East China Institute of Technology, Jiangxi, China)

  • S-R Cheng

    (Cheng Shiu University, Kaohsiung County, Taiwan)

Abstract

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.

Suggested Citation

  • C-C Wu & Y Yin & S-R Cheng, 2013. "Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(1), pages 147-156, January.
    • Handle: RePEc:pal:jorsoc:v:64:y:2013:i:1:p:147-156
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    Citations

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    Cited by:

    1. Zheng Liu & Ji-Bo Wang, 2024. "Single-Machine Scheduling with Simultaneous Learning Effects and Delivery Times," Mathematics, MDPI, vol. 12(16), pages 1-20, August.
    2. Jian-You Xu & Win-Chin Lin & Yu-Wei Chang & Yu-Hsiang Chung & Juin-Han Chen & Chin-Chia Wu, 2023. "A Two-Machine Learning Date Flow-Shop Scheduling Problem with Heuristics and Population-Based GA to Minimize the Makespan," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    3. Ming-Hui Li & Dan-Yang Lv & Yuan-Yuan Lu & Ji-Bo Wang, 2024. "Scheduling with Group Technology, Resource Allocation, and Learning Effect Simultaneously," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    4. Baoyu Liao & Xingming Wang & Xing Zhu & Shanlin Yang & Panos M. Pardalos, 2020. "Less is more approach for competing groups scheduling with different learning effects," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 33-54, January.
    5. Bai, Danyu & Tang, Mengqian & Zhang, Zhi-Hai & Santibanez-Gonzalez, Ernesto DR, 2018. "Flow shop learning effect scheduling problem with release dates," Omega, Elsevier, vol. 78(C), pages 21-38.
    6. Wenjuan Fan & Jun Pei & Xinbao Liu & Panos M. Pardalos & Min Kong, 2018. "Serial-batching group scheduling with release times and the combined effects of deterioration and truncated job-dependent learning," Journal of Global Optimization, Springer, vol. 71(1), pages 147-163, May.
    7. Zhongyi Jiang & Fangfang Chen & Xiandong Zhang, 2022. "Single-machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 116-139, January.
    8. Hongyu He & Mengqi Liu & Ji-Bo Wang, 2017. "Resource constrained scheduling with general truncated job-dependent learning effect," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 626-644, February.
    9. Cheng, Bayi & Zhu, Huijun & Li, Kai & Li, Yongjun, 2019. "Optimization of batch operations with a truncated batch-position-based learning effect," Omega, Elsevier, vol. 85(C), pages 134-143.

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