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Refinement Issues in Stochastic Multistage Linear Programming

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Stochastic Programming Methods and Technical Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 458))

Summary

Linear stochastic multistage programs are considered with uncertain data evolving as a multidimensional discrete-time stochastic process. The associated conditional probability measures are supposed to depend linearly on the past. This ensures convexity of the problem and allows application of barycentric scenario trees. These approximate the discrete-time stochastic process, and provide inner and outer approximation of the value functions.

The main issue is to refine the discretization of the stochastic process efficiently, using the nested optimization and integration of the dynamic, implicitely given value functions. We analyze and illustrate how errors evolve across nodes of the scenario trees.

Research of this report was supported by Schweizerischer Nationalfonds Grant Nr. 21–39’575.93

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Authors and Affiliations

  1. Institute of Operations Research, University of St. Gallen, Holzstrasse 15, CH-9010, St. Gallen, Switzerland

    K. Frauendorfer & Ch. Marohn

Authors
  1. K. Frauendorfer
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  2. Ch. Marohn
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Editors and Affiliations

  1. Fakultät für Luft- und Raumfahrttechnik, Universität der Bundeswehr München, D-85577, Neubiberg/München, Germany

    Kurt Marti

  2. Institut für Operations Research, Universität Zürich, Moussonstraße 15, CH-8044, Zürich, Switzerland

    Peter Kall

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Frauendorfer, K., Marohn, C. (1998). Refinement Issues in Stochastic Multistage Linear Programming. In: Marti, K., Kall, P. (eds) Stochastic Programming Methods and Technical Applications. Lecture Notes in Economics and Mathematical Systems, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45767-8_19

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  • DOI: https://doi.org/10.1007/978-3-642-45767-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63924-4

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