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Nonpreemptive scheduling of independent tasks with prespecified processor allocations

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  • L. Bianco
  • P. Dell'Olmo
  • M. Grazia Speranza

Abstract

In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph‐theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch‐and‐bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.

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  • L. Bianco & P. Dell'Olmo & M. Grazia Speranza, 1994. "Nonpreemptive scheduling of independent tasks with prespecified processor allocations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(7), pages 959-971, December.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:7:p:959-971
    DOI: 10.1002/1520-6750(199412)41:73.0.CO;2-K
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    References listed on IDEAS

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    1. Hermann Buer & Rolf H. Möhring, 1983. "A Fast Algorithm for the Decomposition of Graphs and Posets," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 170-184, May.
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    Cited by:

    1. Lucio Bianco & Paolo Dell'Olmo & Stefano Giordani & Maria Grazia Speranza, 1999. "Minimizing makespan in a multimode multiprocessor shop scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(8), pages 893-911, December.

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