Nicole Gröwe-Kuska, Humboldt-University Berlin
Werner Römisch, Humboldt-University Berlin
(SPEPS)
Springer (Berlin [u.a.])
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| edoc-Server der Humboldt-Universität zu Berlin |
| 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.
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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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