Preemptive Jobs Scheduling on Parallel Machines with Setup Times and Renewable Resources

  • Tomasz Śliwiński
  • Eugeniusz Toczyłowski
Part of the IFIP – The International Federation for Information Processing book series (IFIPAICT, volume 257)

A two-stage algorithm for scheduling preemptive jobs on parallel machines with minimum makespan criterion and requirements for limited renewable resources and existence of sequence dependent setup times is investigated. In the first stage of the algorithm a set of best elementary feasible plans is obtained through column generation. For the second stage we compare genetic algorithms for sequencing elementary plans, where various approximate criterions for calculation minimum makespan are used.


Setup Time Parallel Machine Column Generation Master Problem Sequencing Algorithm 
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  1. 1.
    Dobson G., Karmarkar U., Rummel J.: Batching to minimize flow times on parallel heterogeneous machines. Mgmt Sci. 35 (1989) 607–613.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Figielska E.: Preemptive scheduling with changeovers: using column generation technique and genetic algorithm. Computers & Industrial Engineering 37 (1999) 8184.CrossRefGoogle Scholar
  3. 3.
    Figielska E., Toczyáowski E.: Algorytm szeregowania podzielnych operacji na równolegáych procesorach przy ograniczeniach zasobów zuĪywalnychi odnawialnych. Optymalizacja w zagadnieniach kombinatorycznych, Wyd. WSM (1997) 18–31.Google Scholar
  4. 4.
    Hindi K. S., Toczyáowski E.: Detailed Scheduling of Batch Production in a Cell with Parallel Facilities and Common Renewable Resources. Computers and Industrial Engineering 28 (1995) 839–850.CrossRefGoogle Scholar
  5. 5.
    Oliff M.D.: Disaggregate planning for parallel processors. IIE Trans 19 (1987) 215–219.CrossRefGoogle Scholar
  6. 6.
    So K.: Some heuristics for scheduling jobs on parallel machines with setups. Mgmt Sci. 36 (1990) 467–475.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Toczyáowski E.: Niektóre metody strukturalne optymalizacji do sterowania w dyskretnych systemach wytwarzania. WNT (1989).Google Scholar
  8. 8.
    Toczyáowski E.: Algorithms for preemptive scheduling of independent tasks in the presence of general renewable and consumable resources. Zeszyty Nauk. AGH, Automatyka 59 (1991) 163–172.Google Scholar
  9. 9.
    Toczyáowski E.: Preemptive Scheduling of independent Tasks in the Presence of Setup Times and Renewable Resources. 17th International Symposium on Mathematical Programming ISMP'2000, 7–11 August 2000, Atlanta, USA.Google Scholar

Copyright information

© International Federation for Information Processing 2008

Authors and Affiliations

  • Tomasz Śliwiński
    • 1
  • Eugeniusz Toczyłowski
    • 1
  1. 1.Institute of Control & Computation EngineeringWarsaw University of TechnologyWarsawPoland

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