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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, Hindawi, vol. 2013, pages 1-10, June.
    • Handle: RePEc:hin:jnljam:135610
    DOI: 10.1155/2013/135610
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