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Single-machine scheduling problems with time and position dependent processing times

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  • Xingong Zhang
  • Guangle Yan
  • Wanzhen Huang
  • Guochun Tang

Abstract

We consider single-machine scheduling problems with time and position dependent job processing times. In many industrial settings, the processing time of a job changes due to either job deterioration over time or machine/worker’s learning through experiences. In the models we study, each job has its normal processing time. However, a job’s actual processing time depends on when its processing starts and how many jobs have completed before its start. We prove that the classical SPT (Shortest Processing Time) rule remains optimal when we minimize the makespan or the total completion time. For problems of minimizing the total weighted completion time, the maximum lateness, and the discounted total weighted completion time, we present heuristic sequencing rules and analyze the worst-case bounds for performance ratios. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Xingong Zhang & Guangle Yan & Wanzhen Huang & Guochun Tang, 2011. "Single-machine scheduling problems with time and position dependent processing times," Annals of Operations Research, Springer, vol. 186(1), pages 345-356, June.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:345-356:10.1007/s10479-011-0835-1
    DOI: 10.1007/s10479-011-0835-1
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    References listed on IDEAS

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    Cited by:

    1. Zhang Xingong & Wang Yong & Bai Shikun, 2016. "Single-machine group scheduling problems with deteriorating and learning effect," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2402-2410, July.
    2. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Some results of the worst-case analysis for flow shop scheduling with a learning effect," Annals of Operations Research, Springer, vol. 211(1), pages 481-490, December.
    3. Adam Janiak & Mikhail Kovalyov & Maciej Lichtenstein, 2013. "Strong NP-hardness of scheduling problems with learning or aging effect," Annals of Operations Research, Springer, vol. 206(1), pages 577-583, July.
    4. Radosław Rudek, 2012. "Scheduling problems with position dependent job processing times: computational complexity results," Annals of Operations Research, Springer, vol. 196(1), pages 491-516, July.
    5. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Research on permutation flow shop scheduling problems with general position-dependent learning effects," Annals of Operations Research, Springer, vol. 211(1), pages 473-480, December.

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