Journal of Combinatorial Optimization

, Volume 17, Issue 4, pp 400–416 | Cite as

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

  • Subhash C. Sarin
  • Balaji Nagarajan
  • Sanjay Jain
  • Lingrui Liao


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.


Single machine scheduling Processing time variability Various performance measures Expectation-variance analysis 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Subhash C. Sarin
    • 1
  • Balaji Nagarajan
    • 1
  • Sanjay Jain
    • 1
  • Lingrui Liao
    • 1
  1. 1.Grado Department of Industrial and Systems EngineeringVirginia Tech.BlacksburgUSA

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