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

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

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/135610

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:135610

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