Journal of the Operational Research Society

, Volume 58, Issue 7, pp 938–947

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

Theoretical Paper


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.


scheduling parallel machines availability constraint makespan branch and bound method 


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Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.National Taiwan University of Science and TechnologyTaipeiTaiwan
  2. 2.Jin Wen Institute of TechnologyTaipei County 231Taiwan

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