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Scenario Optimization for Multi-Stage Stochastic Programming Problems

Authors: Ronald Hochreiter

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract

The field of multi-stage stochastic programming provides a rich modelling framework to tackle a broad range of real-world decision problems. In order to numerically solve such programs - once they get reasonably large - the infinite-dimensional optimization problem has to be discretized. The stochastic optimization program generally consists of an optimization model and a stochastic model. In the multi-stage case the stochastic model is most commonly represented as a multi-variate stochastic process. The most common technique to calculate an useable discretization is to generate a scenario tree from the underlying stochastic process. In the first part of the talk we take a look at scenario optimization from the viewpoint of a decision taker, to provide rather non-technical insights into the problem. In the second part of the talk we examplify scenario tree generation by reviewing one specific algorithm based on multi-dimensional facility location applying backward stagewise clustering. An example from the area of financial engineering concludes the talk.

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Ronald Hochreiter. Scenario Optimization for Multi-Stage Stochastic Programming Problems. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{hochreiter:DagSemProc.05031.26,
  author =	{Hochreiter, Ronald},
  title =	{{Scenario Optimization for Multi-Stage Stochastic Programming Problems}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.26},
  URN =		{urn:nbn:de:0030-drops-614},
  doi =		{10.4230/DagSemProc.05031.26},
  annote =	{Keywords: Stochastic programming, scenario generation, facility location, financial engineering}
}

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Scenario Optimization for Multi-Stage Stochastic Programming Problems

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