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Single Machine Problem with Multi‐Rate‐Modifying Activities under a Time‐Dependent Deterioration

Author

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  • M. Huang
  • Huaping Wu
  • Vincent Cho
  • W. H. Ip
  • Xingwei Wang
  • C. K. Ng

Abstract

The single machine scheduling problem with multi‐rate‐modifying activities under a time‐dependent deterioration to minimize makespan is studied. After examining the characteristics of the problem, a number of properties and a lower bound are proposed. A branch and bound algorithm and a heuristic algorithm are used in the solution, and two special cases are also examined. The computational experiments show that, for the situation with a rate‐modifying activity, the proposed branch and bound algorithm can solve situations with 50 jobs within a reasonable time, and the heuristic algorithm can obtain the near‐optimal solution with an error percentage less than 0.053 in a very short time. In situations with multi‐rate‐modifying activities, the proposed branch and bound algorithm can solve the case with 15 jobs within a reasonable time, and the heuristic algorithm can obtain the near‐optimal with an error percentage less than 0.070 in a very short time. The branch and bound algorithm and the heuristic algorithm are both shown to be efficient and effective.

Suggested Citation

  • M. Huang & Huaping Wu & Vincent Cho & W. H. Ip & Xingwei Wang & C. K. Ng, 2013. "Single Machine Problem with Multi‐Rate‐Modifying Activities under a Time‐Dependent Deterioration," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:135610
    DOI: 10.1155/2013/135610
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    References listed on IDEAS

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    1. Ji-Bo Wang & T. C. Edwin Cheng, 2007. "Scheduling Problems With The Effects Of Deterioration And Learning," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 245-261.
    2. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    3. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
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