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Multiprocessor Scheduling with Availability Constraints

In: Operations Research Proceedings 2012

Author

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  • Liliana Grigoriu

    (University Siegen)

Abstract

When scheduling on parallel machines, these may exhibit periods of unavailability, due to maintenance or failures, or due to jobs that must be executed at certain predefined times. We consider the problem of non-preemptively scheduling a given set of tasks on identical processors with periods of unavailability to minimize the maximum completion time. This problem is strongly NP-hard, thus polynomial approximation algorithms are being studied for its solution. Often considered approximation algorithms for multiprocessor scheduling and generalizations thereof are LPT (largest processing time first) and Multifit with their variants. We give a simple polynomial Multifit-based algorithm, the schedules of which end within 1.5 the maximum between the end of the optimal schedule and the latest end of a downtime when there are at most two downtimes on each machine. Even when there is at most one downtime on each machine, no polynomial algorithm can insure a better worst-case bound for this problem unless P=NP. For the case when there is at most one downtime on each machine we also present a simple LPT-based algorithm which has the same property. We also give details of the upper bound proofs.

Suggested Citation

  • Liliana Grigoriu, 2014. "Multiprocessor Scheduling with Availability Constraints," Operations Research Proceedings, in: Stefan Helber & Michael Breitner & Daniel Rösch & Cornelia Schön & Johann-Matthias Graf von der Schu (ed.), Operations Research Proceedings 2012, edition 127, pages 423-428, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-00795-3_63
    DOI: 10.1007/978-3-319-00795-3_63
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