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A note on single-machine total completion time problem with general deteriorating function

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Abstract

In this paper, we consider the single-machine scheduling problem with a deteriorating function. By the deteriorating function, we mean that the actual job processing time is a function of jobs already processed. We show that the total completion time minimization problem for a ≥ 1 remains polynomially solvable under the proposed model, where a denotes the deterioration rate. For the case of 0 < a < 1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times. We use the classical smallest processing time first rule as a heuristic algorithm for the case of 0 < a < 1 and analyze its worst-case bound.

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Authors and Affiliations

  1. School of Science, Shenyang Institute of Aeronautical Engineering, Shenyang, 110136, People’s Republic of China

    Ji-Bo Wang, Li-Yan Wang, Dan Wang, Xue Huang & Xue-Ru Wang

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Li-Yan Wang

Authors
  1. Ji-Bo Wang
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  2. Li-Yan Wang
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  3. Dan Wang
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  4. Xue Huang
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  5. Xue-Ru Wang
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Correspondence to Ji-Bo Wang.

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Wang, JB., Wang, LY., Wang, D. et al. A note on single-machine total completion time problem with general deteriorating function. Int J Adv Manuf Technol 44, 1213–1218 (2009). https://doi.org/10.1007/s00170-008-1918-2

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  • DOI: https://doi.org/10.1007/s00170-008-1918-2

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