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Parallel machine scheduling: A probabilistic analysis

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  • Nanda Piersma
  • H. Edwin Romeijn

Abstract

The minimum makespan of the general parallel machine scheduling problem with m machines and n jobs is studied. As for a number of other important combinatorial problems, the theory of empirical processes proves to be a very elegant and powerful tool for the probabilistic analysis of the solution value. It is used in this paper to derive a scheduling constant θ such that, for random processing times, the minimum makespan almost surely grows as θn when n goes to infinity. Moreover, a thorough probabilistic analysis is performed on the difference between the minimum makespan and θn. Explicit expressions for the scheduling constant are given for an arbitrary number of unrelated machines with identically distributed processing times (with an increasing failure rate), and for an arbitrary number of uniform machines and generally distributed processing times. © 1996 John Wiley & Sons, Inc.

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  • Nanda Piersma & H. Edwin Romeijn, 1996. "Parallel machine scheduling: A probabilistic analysis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 897-916, September.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:6:p:897-916
    DOI: 10.1002/(SICI)1520-6750(199609)43:63.0.CO;2-#
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    References listed on IDEAS

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    1. Wansoo T. Rhee, 1988. "Optimal Bin Packing with Items of Random Sizes," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 140-151, February.
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    Cited by:

    1. Nanda Piersma, 1999. "A Probabilistic Analysis of the Capacitated Facility Location Problem," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 31-50, July.
    2. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.

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