Stochastic scheduling problems I - General strategies

R. H. Möhring, F. J. Radermacher, G. Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

The paper contains an introduction to recent developments in the theory of non-preemptive stochastic scheduling problems. The topics covered are: arbitrary joint distributions of activity durations, arbitrary regular measures of performance and arbitrary precedence and resource constraints. The possible instability of the problem is demonstrated and hints are given on stable classes of strategies available, including the combinatorial vs. analytical characterization of such classes. Given this background, the main emphasis of the paper is on the monotonicity behaviour of the model and on the existence of optimal strategies. Existing results are presented and generalized, in particular w.r.t. the cases of lower semicontinuous performance measures or joint duration distributions having a Lebesgue density.

Original languageEnglish
Pages (from-to)193-260
Number of pages68
JournalMathematical Methods of Operations Research
Volume28
Issue number7
DOIs
StatePublished - Nov 1984
Externally publishedYes

Keywords

  • Analytic behaviour of strategies
  • continuous strategies
  • ES strategies
  • machine idleness
  • MES strategies
  • monotonicity behaviour
  • optimal strategies
  • preselectivity
  • regular measure of performance
  • scheduling problems
  • stability
  • stochastic dynamic optimization
  • stochastic scheduling
  • stochastically ordered distributions

ASJC Scopus subject areas

  • Engineering (all)

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