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A note on parallel-machine scheduling with deteriorating jobs

Author

Listed:
  • A A K Jeng

    (National Chiao Tung University)

  • B M T Lin

    (Department of Information and Finance Management)

Abstract

We consider a parallel-machine scheduling problem of minimizing the total completion time. The processing time of a job is a linear function of its starting time and deterioration rate. This problem is known to be NP-hard, even for the case with two machines. In this note, we generalize an existing lower bound for the two-machine case to the general case with an arbitrary number of machines. Despite the generalization concerning machine number, our bound has one extra term that makes our bound tighter than the existing one.

Suggested Citation

  • A A K Jeng & B M T Lin, 2007. "A note on parallel-machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 824-826, June.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:6:d:10.1057_palgrave.jors.2602208
    DOI: 10.1057/palgrave.jors.2602208
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    References listed on IDEAS

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    1. 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.
    2. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
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    Citations

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    Cited by:

    1. Su, Ling-Huey & Lien, Chun-Yuan, 2009. "Scheduling parallel machines with resource-dependent processing times," International Journal of Production Economics, Elsevier, vol. 117(2), pages 256-266, February.
    2. J-B Wang & J-J Wang & P Ji, 2011. "Scheduling jobs with chain precedence constraints and deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1765-1770, September.
    3. Gawiejnowicz, Stanislaw & Kurc, Wieslaw & Pankowska, Lidia, 2009. "Equivalent time-dependent scheduling problems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 919-929, August.
    4. Ming Liu & Feifeng Zheng & Chengbin Chu & Jiantong Zhang, 2012. "An FPTAS for uniform machine scheduling to minimize makespan with linear deterioration," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 483-492, May.
    5. Wu, Chin-Chia & Lee, Wen-Chiung, 2008. "Single-machine group-scheduling problems with deteriorating setup times and job-processing times," International Journal of Production Economics, Elsevier, vol. 115(1), pages 128-133, September.
    6. Li, Yongqiang & Li, Gang & Sun, Linyan & Xu, Zhiyong, 2009. "Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times," International Journal of Production Economics, Elsevier, vol. 118(2), pages 424-429, April.
    7. 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.
    8. Epstein, Leah & Levin, Asaf, 2011. "Scheduling with processing set restrictions: PTAS results for several variants," International Journal of Production Economics, Elsevier, vol. 133(2), pages 586-595, October.
    9. Mosheiov, Gur, 2012. "A note: Multi-machine scheduling with general position-based deterioration to minimize total load," International Journal of Production Economics, Elsevier, vol. 135(1), pages 523-525.

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