General stochastic single-machine scheduling with regular cost functions

X. Zhou*, X. Cai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


We examine a stochastic scheduling model with n jobs and a single machine, where the processing times of the jobs are random variables with arbitrary distributions, and the machine is subject to stochastic breakdowns. Two types of regular performance measures, the total cost and the maximum cost, with general cost functions are investigated. We derive conditions under which a sequence in nondecreasing stochastic order of processing times minimizes the total expected cost, whereas a sequence in nondecreasing stochastic order of due dates minimizes the maximum expected cost. In addition, results on almost sure minimization of the total stochastic cost or the maximum stochastic cost are also provided. Applications of the general results to various special cases with commonly studied measures like mean weighted flowtime, mean weighted tardiness, weighted number of tardy jobs, maximum tardiness, etc., are discussed, which extend the previous results on these cases to more general situations.

Original languageEnglish
Pages (from-to)95-108
Number of pages14
JournalMathematical and Computer Modelling
Issue number3
Publication statusPublished - Aug 1997
Externally publishedYes


  • Due dates
  • Regular measures
  • Single machine
  • Stochastic scheduling


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