Mathematical Programming

, Volume 95, Issue 3, pp 493–511 | Cite as

Scenario reduction in stochastic programming

  • J. Dupačová
  • N. Gröwe-Kuska
  • W. Römisch


 Given a convex stochastic programming problem with a discrete initial probability distribution, the problem of optimal scenario reduction is stated as follows: Determine a scenario subset of prescribed cardinality and a probability measure based on this set that is the closest to the initial distribution in terms of a natural (or canonical) probability metric. Arguments from stability analysis indicate that Fortet-Mourier type probability metrics may serve as such canonical metrics. Efficient algorithms are developed that determine optimal reduced measures approximately. Numerical experience is reported for reductions of electrical load scenario trees for power management under uncertainty. For instance, it turns out that after 50% reduction of the scenario tree the optimal reduced tree still has about 90% relative accuracy.


Programming Problem Initial Distribution Stochastic Programming Initial Probability Power Management 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • J. Dupačová
    • 1
  • N. Gröwe-Kuska
    • 2
  • W. Römisch
    • 3
  1. 1.Charles University Prague, Department of Probability and Mathematical Statistics, 18675 Prague 8, Czech Republic, e-mail: dupacova@karlin.mff.cuni.czCZ
  2. 2.Humboldt-University Berlin, Institute of Mathematics, 10099 Berlin, Germany, e-mail:
  3. 3.Humboldt-University Berlin, Institute of Mathematics, 10099 Berlin, Germany, e-mail:

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