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Scheduling jobs with piecewise linear decreasing processing times

Author

Listed:
  • T.C. Edwin Cheng
  • Qing Ding
  • Mikhail Y. Kovalyov
  • Aleksander Bachman
  • Adam Janiak

Abstract

We study the problems of scheduling a set of nonpreemptive jobs on a single or multiple machines without idle times where the processing time of a job is a piecewise linear nonincreasing function of its start time. The objectives are the minimization of makespan and minimization of total job completion time. The single machine problems are proved to be NP‐hard, and some properties of their optimal solutions are established. A pseudopolynomial time algorithm is constructed for makespan minimization. Several heuristics are derived for both total completion time and makespan minimization. Computational experiments are conducted to evaluate their efficiency. NP‐hardness proofs and polynomial time algorithms are presented for some special cases of the parallel machine problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 531–554, 2003

Suggested Citation

  • T.C. Edwin Cheng & Qing Ding & Mikhail Y. Kovalyov & Aleksander Bachman & Adam Janiak, 2003. "Scheduling jobs with piecewise linear decreasing processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 531-554, September.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:6:p:531-554
    DOI: 10.1002/nav.10073
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    References listed on IDEAS

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    1. W. A. Horn, 1973. "Technical Note—Minimizing Average Flow Time with Parallel Machines," Operations Research, INFORMS, vol. 21(3), pages 846-847, June.
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    4. K. D. Glazebrook, 1992. "Single‐machine scheduling of stochastic jobs subject to deterioration or delay," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 613-633, August.
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    6. Wieslaw Kubiak & Steef van de Velde, 1998. "Scheduling deteriorating jobs to minimize makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(5), pages 511-523, August.
    7. Bachman, Aleksander & Janiak, Adam, 2000. "Minimizing maximum lateness under linear deterioration," European Journal of Operational Research, Elsevier, vol. 126(3), pages 557-566, November.
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    Cited by:

    1. Baoyu Liao & Qingru Song & Jun Pei & Shanlin Yang & Panos M. Pardalos, 2020. "Parallel-machine group scheduling with inclusive processing set restrictions, outsourcing option and serial-batching under the effect of step-deterioration," Journal of Global Optimization, Springer, vol. 78(4), pages 717-742, December.
    2. C. Ng & Q. Ding & T. Cheng & S. Lam, 2012. "Preemptive repayment policy for multiple loans," Annals of Operations Research, Springer, vol. 192(1), pages 141-150, January.
    3. Jun Pei & Qingru Song & Baoyu Liao & Xinbao Liu & Panos M. Pardalos, 2021. "Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration," Annals of Operations Research, Springer, vol. 298(1), pages 407-444, March.
    4. Hongfeng Wang & Min Huang & Junwei Wang, 2019. "An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2733-2742, October.
    5. Helmut A. Sedding, 2020. "Scheduling jobs with a V-shaped time-dependent processing time," Journal of Scheduling, Springer, vol. 23(6), pages 751-768, December.
    6. Dar-Li Yang & Wen-Hung Kuo, 2009. "Single-machine scheduling with both deterioration and learning effects," Annals of Operations Research, Springer, vol. 172(1), pages 315-327, November.

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