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SPEPS Preprint

Author(s): Jitka Dupacová, Charles University
Nicole Gröwe-Kuska, Humboldt-University Berlin
Werner Römisch, Humboldt-University Berlin
Title: Scenario reduction in stochastic programming: An approach using probability metrics
Date of Acceptance: 14.08.2000
Submission Date: 12.07.2000
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): quantitative stability, Stochastic programming, electrical load scenario tree, scenario reduction, Fortet-Mourier metrics, transportation problem
Appeared in: Mathematical Programming 3 (Vol. 95, 2003)
Springer (Berlin [u.a.])
Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex  

Abstract (eng):
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 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 a 50% reduction of the scenario tree the optimal reduced tree still has about 90% of relative accuracy.
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