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Minimizing makespan for two parallel machines with job limit on each availability interval

Author

Listed:
  • C-J Liao

    (National Taiwan University of Science and Technology)

  • C-M Chen

    (National Taiwan University of Science and Technology)

  • C-H Lin

    (Jin Wen Institute of Technology)

Abstract

We consider the problem of scheduling jobs on two parallel machines that are not continuously available for processing. The machine is not available after processing a fixed number of jobs in order to make precision adjustment of machines such as in wafer manufacturing, to reload the feeder in printed circuit board production, or to undertake any other maintenance works such as cleaning and safety inspections. The objective of the problem is to minimize the makespan. Two different scheduling horizons are investigated for this problem. For the short-term scheduling horizon, we consider only the time period before the unavailability interval, while for the long-term horizon, machines are allowed to restart processing after the unavailability interval. For both cases, which are strongly NP-hard, exact optimization algorithms based on the branch and bound method are proposed. Although the algorithms have exponential time complexities, computational results show that they can solve optimally the various-sized problems in reasonable computation time.

Suggested Citation

  • C-J Liao & C-M Chen & C-H Lin, 2007. "Minimizing makespan for two parallel machines with job limit on each availability interval," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 938-947, July.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:7:d:10.1057_palgrave.jors.2602209
    DOI: 10.1057/palgrave.jors.2602209
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    References listed on IDEAS

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    1. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    2. Johnny C. Ho & Johnny S. Wong, 1995. "Makespan minimization for m parallel identical processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 935-948, September.
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    Cited by:

    1. Lee, Cheng-Hsiung & Liao, Ching-Jong & Chung, Tsui-Ping, 2014. "Scheduling with multi-attribute setup times on two identical parallel machines," International Journal of Production Economics, Elsevier, vol. 153(C), pages 130-138.
    2. A J Ruiz-Torres & F J López & P J Wojciechowski & J C Ho, 2010. "Parallel machine scheduling problems considering regular measures of performance and machine cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 849-857, May.
    3. Sandeep Kumar & Bhupesh Kumar Lad, 2017. "Integrated production and maintenance planning for parallel machine system considering cost of rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 834-846, July.

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