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Sequencing jobs with random processing times to minimize weighted completion time variance

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  • X. Cai
  • S. Zhou

Abstract

We examine the problem of sequencing a set of jobs on a single machine, where each job has a random processing time and is associated with a known, job-dependent weight. The objective is to minimize the expectation of the weighted variance of job completion times. We establish the NP-completeness of this problem, and further show that the problem under some compatible conditions is NP-complete in the ordinary sense. We introduce the concept of a W-shaped solution for the problem and find that an optimal W-shaped sequence exists under the compatible conditions. We propose an exact algorithm, based on this W-shaped property, which can generate an optimal solution in pseudopolynomial time. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • X. Cai & S. Zhou, 1997. "Sequencing jobs with random processing times to minimize weighted completion time variance," Annals of Operations Research, Springer, vol. 70(0), pages 241-260, April.
    • Handle: RePEc:spr:annopr:v:70:y:1997:i:0:p:241-260:10.1023/a:1018926305578
    DOI: 10.1023/A:1018926305578
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