Annals of Operations Research

, Volume 213, Issue 1, pp 173–186 | Cite as

Makespan minimization for parallel machines scheduling with multiple availability constraints

  • Navid Hashemian
  • Claver DialloEmail author
  • Béla Vizvári


The problem of makespan minimization for parallel machines scheduling with multiple planned nonavailability periods in the case of resumable jobs is considered. In the current state of the literature, there is a limited number of models and algorithms dealing with this problem and only for very small problem size, and nonavailability limited to some machines. The problem is first formulated as a mixed integer linear programming model and optimally solved using CPLEX for small to moderately large size problems with multiple availability constraints on all machines. An implicit enumeration algorithm using the lexicographic order is then designed to solve large-scale problems. Numerical results are obtained for several experiments and they show the validity and performance improvements procured by both the MILP model and the new enumeration algorithm.


Parallel machines Availability constraints Makespan Scheduling 



The authors would like to thank the anonymous referees, the editors and Dr. Eldon Gunn for their useful comments and suggestions. This research work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant 356664–2008.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Navid Hashemian
    • 1
  • Claver Diallo
    • 1
    Email author
  • Béla Vizvári
    • 2
  1. 1.Dalhousie UniversityHalifaxCanada
  2. 2.Eastern Mediterranean UniversityFamagusta Mersin 10Turkey

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