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Complexity and approximability of scheduling resumable proportionally deteriorating jobs

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  • Gawiejnowicz, Stanislaw
  • Kononov, Alexander

Abstract

A set of independent, resumable and proportionally deteriorating jobs is to be executed on a single machine. The machine is not continuously available for processing but the number of non-availability periods, the start time and end time of each period are known in advance. The criterion of schedule optimality is the maximum completion time. It is proved that the decision version of the problem with a single non-availability period is ordinarily -complete. It is also proved that for the problem with a single non-availability period there exists a fully polynomial-time approximation scheme. Finally, it is proved that for the problem with two or more non-availability periods there does not exist a polynomial-time approximation algorithm with a constant worst-case ratio, unless .

Suggested Citation

  • Gawiejnowicz, Stanislaw & Kononov, Alexander, 2010. "Complexity and approximability of scheduling resumable proportionally deteriorating jobs," European Journal of Operational Research, Elsevier, vol. 200(1), pages 305-308, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:1:p:305-308
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    References listed on IDEAS

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    1. Gawiejnowicz, Stanislaw, 2007. "Scheduling deteriorating jobs subject to job or machine availability constraints," European Journal of Operational Research, Elsevier, vol. 180(1), pages 472-478, July.
    2. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
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    Cited by:

    1. Yang, Suh-Jenq & Yang, Dar-Li, 2010. "Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities," Omega, Elsevier, vol. 38(6), pages 528-533, December.
    2. Stanisław Gawiejnowicz & Alexander Kononov, 2014. "Isomorphic scheduling problems," Annals of Operations Research, Springer, vol. 213(1), pages 131-145, February.
    3. Wang, Ting & Baldacci, Roberto & Lim, Andrew & Hu, Qian, 2018. "A branch-and-price algorithm for scheduling of deteriorating jobs and flexible periodic maintenance on a single machine," European Journal of Operational Research, Elsevier, vol. 271(3), pages 826-838.
    4. Cheng, Mingbao & Tadikamalla, Pandu R. & Shang, Jennifer & Zhang, Shaqing, 2014. "Bicriteria hierarchical optimization of two-machine flow shop scheduling problem with time-dependent deteriorating jobs," European Journal of Operational Research, Elsevier, vol. 234(3), pages 650-657.
    5. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    6. Min Ji & Chou-Jung Hsu & Dar-Li Yang, 2013. "Single-machine scheduling with deteriorating jobs and aging effects under an optional maintenance activity consideration," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 437-447, October.
    7. Ma, Ran & Tao, Jiping & Yuan, Jinjiang, 2016. "Online scheduling with linear deteriorating jobs to minimize the total weighted completion time," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 570-583.
    8. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    9. S Gawiejnowicz & W-C Lee & C-L Lin & C-C Wu, 2011. "Single-machine scheduling of proportionally deteriorating jobs by two agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1983-1991, November.

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