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Stability and Scenario Trees for Multistage Stochastic Programs

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Book cover Stochastic Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 150))

Abstract

By extending the stability analysis of Heitsch et al. (2006) for multistage stochastic programs we show that their (approximate) solution sets behave stable with respect to the sum of an $L_r$-distance and a filtration distance. Based on such stability results we suggest a scenario tree generation method for the (multivariate) stochastic input process. It starts with an initial scenario set and consists of a recursive deletion and branching procedure which is controlled by bounding the approximation error. Some numerical experience for generating scenario trees in electricity portfolio management is reported.

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Acknowledgments

This work was supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin, the BMBF under the grant 03SF0312E, and a grant of EDF – Electricité de France.

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Authors and Affiliations

  1. Institute of Mathematics, Humboldt-University Berlin, Berlin, Germany

    Holger Heitsch & Werner Römisch

Authors
  1. Holger Heitsch
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  2. Werner Römisch
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Correspondence to Holger Heitsch .

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Editors and Affiliations

  1. Dept. Management Science & Engineering, Stanford University, Stanford, 94305, California, USA

    Gerd Infanger

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Heitsch, H., Römisch, W. (2010). Stability and Scenario Trees for Multistage Stochastic Programs. In: Infanger, G. (eds) Stochastic Programming. International Series in Operations Research & Management Science, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1642-6_7

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