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Permutation Flow Shop Problem with Shortening Job Processing Times

Author

Listed:
  • Zhenyou Wang

    (Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, P. R. China)

  • Cai-Min Wei

    (Department of Mathematics, Shantou University, Shantou 515063, P. R. China3Guangdong Provincial Key Lab of Digital Signals and Image Processing, Shantou University, Shantou, Guangdong, 515063, P. R. China)

  • Yuan-Yuan Lu

    (College of Mathematics, Jilin Normal University, Siping, Jilin 136000, P. R. China)

Abstract

In this paper, we consider a three-machine makespan minimization permutation flow shop scheduling problem with shortening job processing times. Shortening job processing times means that its processing time is a nonincreasing function of its execution start time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and two lower bounds are developed to construct a branch-and-bound (B&B) algorithm. Furthermore, we propose a heuristic algorithm to overcome the inefficiency of the branch-and-bound algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:04:n:s0217595916500329
    DOI: 10.1142/S0217595916500329
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    References listed on IDEAS

    as
    1. 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.
    2. Chuanli Zhao & Hengyong Tang, 2015. "Due-Window Assignment for a Single Machine Scheduling with Both Deterioration and Positional Effects," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-11.
    3. Xuyin Wang & Xiangpei Hu & Weiguo Liu, 2015. "Scheduling with Deteriorating Jobs and Non-Simultaneous Machine Available Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-13, December.
    4. 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.
    5. Ji-Bo Wang & Jian-Jun Wang, 2015. "Research on scheduling with job-dependent learning effect and convex resource-dependent processing times," International Journal of Production Research, Taylor & Francis Journals, vol. 53(19), pages 5826-5836, October.
    6. 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.
    7. Edward Ignall & Linus Schrage, 1965. "Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems," Operations Research, INFORMS, vol. 13(3), pages 400-412, June.
    8. 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.
    9. Xin-Jun Li & Jian-Jun Wang & Xue-Ru Wang, 2015. "Single-Machine Scheduling with Learning Effect, Deteriorating Jobs and Convex Resource Dependent Processing Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-12.
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    11. Jan-Yee Kung & Ming-Hung Shu, 2015. "Some Scheduling Problems on a Single Machine with General Job Effects of Position-Dependent Learning and Start-Time-Dependent Deterioration," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-21.
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