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Single-machine scheduling with resource-dependent processing times and multiple unavailability periods

Author

Listed:
  • Byung-Cheon Choi

    (Chungnam National University)

  • Myoung-Ju Park

    (Kyung Hee University)

Abstract

We consider a single-machine scheduling problem with multiple unavailability periods such that the processing time of each job is inversely proportional to the kth power of its own resource consumption amount. The objective is to minimize the sum of the makespan and the total resource consumption cost. For every $$k>0$$ k > 0 , we show that the problem with one unavailability period is NP-hard while it admits a fully polynomial-time approximation scheme. Furthermore, we analyze the (in)approximability for the case with multiple unavailability periods. For every $$k>0$$ k > 0 , we show that the problem with an arbitrary number of unavailability periods is strongly NP-hard. Finally, we extend the results to the problem of minimizing the makespan with a constraint on the total resource consumption cost.

Suggested Citation

  • Byung-Cheon Choi & Myoung-Ju Park, 2022. "Single-machine scheduling with resource-dependent processing times and multiple unavailability periods," Journal of Scheduling, Springer, vol. 25(2), pages 191-202, April.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:2:d:10.1007_s10951-022-00723-z
    DOI: 10.1007/s10951-022-00723-z
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    References listed on IDEAS

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    1. R. G. Vickson, 1980. "Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine," Operations Research, INFORMS, vol. 28(5), pages 1155-1167, October.
    2. T.C.E. Cheng & A. Janiak, 2000. "A permutation flow-shop scheduling problem with convex models of operation processing times," Annals of Operations Research, Springer, vol. 96(1), pages 39-60, November.
    3. Shabtay, Dvir & Kaspi, Moshe, 2006. "Parallel machine scheduling with a convex resource consumption function," European Journal of Operational Research, Elsevier, vol. 173(1), pages 92-107, August.
    4. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    5. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    6. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
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    Cited by:

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