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Minimizing total completion time in two‐processor task systems with prespecified processor allocations

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  • Xiaoqiang Cai
  • Chung‐Yee Lee
  • Chung‐Lun Li

Abstract

We consider the problem of scheduling multiprocessor tasks with prespecified processor allocations to minimize the total completion time. The complexity of both preemptive and nonpreemptive cases of the two‐processor problem are studied. We show that the preemptive case is solvable in O(n log n) time. In the nonpreemptive case, we prove that the problem is NP‐hard in the strong sense, which answers an open question mentioned in Hoogeveen, van de Velde, and Veltman (1994). An efficient heuristic is also developed for this case. The relative error of this heuristic is at most 100%. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 231–242, 1998

Suggested Citation

  • Xiaoqiang Cai & Chung‐Yee Lee & Chung‐Lun Li, 1998. "Minimizing total completion time in two‐processor task systems with prespecified processor allocations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(2), pages 231-242, March.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:2:p:231-242
    DOI: 10.1002/(SICI)1520-6750(199803)45:23.0.CO;2-9
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    References listed on IDEAS

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    1. Brucker, Peter & Kramer, Andreas, 1996. "Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems," European Journal of Operational Research, Elsevier, vol. 90(2), pages 214-226, April.
    2. L. Bianco & J. Blazewicz & P. Dell'Olmo & M. Drozdowski, 1997. "Preemptive multiprocessor task scheduling with release times and time windows," Annals of Operations Research, Springer, vol. 70(0), pages 43-55, April.
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