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Minimizing the number of machines for minimum length schedules

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  • Finke, Gerd
  • Lemaire, Pierre
  • Proth, Jean-Marie
  • Queyranne, Maurice

Abstract

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various particular cases.

Suggested Citation

  • Finke, Gerd & Lemaire, Pierre & Proth, Jean-Marie & Queyranne, Maurice, 2009. "Minimizing the number of machines for minimum length schedules," European Journal of Operational Research, Elsevier, vol. 199(3), pages 702-705, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:3:p:702-705
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    References listed on IDEAS

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    1. T. C. Hu, 1961. "Parallel Sequencing and Assembly Line Problems," Operations Research, INFORMS, vol. 9(6), pages 841-848, December.
    2. Leo G. Kroon & Marc Salomon & Luk N. Van Wassenhove, 1997. "Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem," Operations Research, INFORMS, vol. 45(4), pages 624-638, August.
    3. Aziz Moukrim, 2000. "Upper bound on the number of processors for scheduling with interprocessor communication delays," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 99-113, September.
    4. A. Moukrim, 1999. "On the minimum number of processors for scheduling problems with communicationdelays," Annals of Operations Research, Springer, vol. 86(0), pages 455-472, January.
    5. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
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    Cited by:

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    2. Shi, Yuhui & Reich, Daniel & Epelman, Marina & Klampfl, Erica & Cohn, Amy, 2017. "An analytical approach to prototype vehicle test scheduling," Omega, Elsevier, vol. 67(C), pages 168-176.

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