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Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability

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Listed:
  • Subhash C. Sarin

    (Virginia Tech.)

  • Balaji Nagarajan

    (Virginia Tech.)

  • Sanjay Jain

    (Virginia Tech.)

  • Lingrui Liao

    (Virginia Tech.)

Abstract

In this paper, we present closed-form expressions, wherever possible, or devise algorithms otherwise, to determine the expectation and variance of a given schedule on a single machine. We consider a variety of completion time and due date-based objectives. The randomness in the scheduling process is due to variable processing times with known means and variances of jobs and, in some cases, a known underlying processing time distribution. The results that we present in this paper can enable evaluation of a schedule in terms of both the expectation and variance of a performance measure considered, and thereby, aid in obtaining a stable schedule. Additionally, the expressions and algorithms that are presented, can be incorporated in existing scheduling algorithms in order to determine expectation-variance efficient schedules.

Suggested Citation

  • Subhash C. Sarin & Balaji Nagarajan & Sanjay Jain & Lingrui Liao, 2009. "Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 400-416, May.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:4:d:10.1007_s10878-007-9122-0
    DOI: 10.1007/s10878-007-9122-0
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    References listed on IDEAS

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    4. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1992. "Expectation-variance analyss of job sequences under processing time uncertainty," International Journal of Production Economics, Elsevier, vol. 28(3), pages 289-297, December.
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