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On three-machine flow shop scheduling with deteriorating jobs

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  • Wang, Ling
  • Sun, Lin-Yan
  • Sun, Lin-Hui
  • Wang, Ji-Bo

Abstract

In this paper, we consider a three-machine permutation flow shop scheduling problem under simple linear deterioration. By a simple linear deterioration function, we mean that the processing time of a job is a simple linear function of its execution start time. The objective is to find a sequence that minimizes makespan. This problem is well known NP-hard. Optimal schedules are obtained for some special cases. For the general case, several dominance properties and two lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. Moreover, a heuristic algorithm is proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational experiments on randomly generated problems is conducted to evaluate the branch-and-bound algorithm and heuristic algorithm. The analysis shows that the proposed heuristic algorithm performs effectively and efficiently.

Suggested Citation

  • Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
    • Handle: RePEc:eee:proeco:v:125:y:2010:i:1:p:185-189
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    References listed on IDEAS

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    Cited by:

    1. Abbasali Jafari-Nodoushan & Hassan Khademi Zare & M. M. Lotfi & R. Tavakkoli-Moghaddam, 2021. "Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop," SN Operations Research Forum, Springer, vol. 2(4), pages 1-29, December.
    2. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.
    3. Janiak, Adam & Krysiak, Tomasz, 2012. "Scheduling jobs with values dependent on their completion times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 231-241.
    4. Lee, Wen-Chiung & Chung, Yu-Hsiang, 2013. "Permutation flowshop scheduling to minimize the total tardiness with learning effects," International Journal of Production Economics, Elsevier, vol. 141(1), pages 327-334.
    5. Na Yin & Liying Kang, 2015. "Minimizing Makespan in Permutation Flow Shop Scheduling with Proportional Deterioration," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-12, December.
    6. Gur Mosheiov & Daniel Oron, 2020. "Scheduling problems with a weight-modifying-activity," Annals of Operations Research, Springer, vol. 295(2), pages 737-745, December.
    7. Zhao, Chuanli & Tang, Hengyong, 2012. "Two-machine flow shop scheduling with deteriorating jobs and chain precedence constraints," International Journal of Production Economics, Elsevier, vol. 136(1), pages 131-136.
    8. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    9. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    10. Zhenyou Wang & Cai-Min Wei & Yuan-Yuan Lu, 2016. "Permutation Flow Shop Problem with Shortening Job Processing Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-14, August.

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