Advertisement

Stochastic Extensions to FlopC++

  • Christian WolfEmail author
  • Achim Koberstein
  • Tim Hultberg
Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

We extend the open-source modelling language FlopC++, which is part of the COIN-OR project, to support multi-stage stochastic programs with recourse. We connect the stochastic version of FlopC++ to the existing COIN class stochastic modelling interface (SMI) to provide a direct interface to specialized solution algorithms. The new stochastic version of FlopC++ can be used to specify scenario-based problems and distribution-based problems with independent random variables. A data-driven scenario tree generation method transforms a given scenario fan, a collection of different data paths with specified probabilities, into a scenario tree. We illustrate our extensions by means of a two-stage mixed integer strategic supply chain design problem and a multi-stage investment model.

Keywords

Stochastic Program Scenario Tree Stochastic Version Multistage Stochastic Program Deterministic Equivalent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.V. Dmitruk. Quadratic Conditions for a Weak Minimum for Singular Regimes in Optimal Control Problems. Soviet Math. Doklady, v. 18, no. 2, 1977.Google Scholar
  2. 2.
    V.A. Dubovitskij. Necessary and Sufficient Conditions for a Pontryagin Minimum in Problems of Optimal Control with Singular Regimes and Generalized Controls (in Russian). Us-pekhi Mat. Nauk, v. 37, no. 3, p. 185–186, 1982.Google Scholar
  3. 3.
    A.V. Dmitruk. Quadratic Conditions for a Pontryagin Minimum in an Optimal Control Problem, Linear in the Control. Math. of USSR, Izvestija, v. 28, no. 2, 1987.Google Scholar
  4. 4.
    A.V. Dmitruk. Quadratic Order Conditions of a Local Minimum for Singular Extremals in a General Optimal Control Problem. Proc. Symposia in Pure Math., v. 64 “Diff. Geometry and Control(G.Ferreyra et al., eds.), American Math. Society, p. 163–198, 1999.Google Scholar
  5. 5.
    A.A. Milyutin and N.P. Osmolovskii. Calculus of Variations and Optimal Control. American Math. Society, Providence, RI, 1999.Google Scholar
  6. 6.
    A.V. Dmitruk. Jacobi Type Conditions for Singular Extremals. Control and Cybernetics, v. 37, no. 2, p. 285–306, 2008.Google Scholar
  7. 7.
    A.V. Dmitruk and K. K. Shishov. Analysis of a Quadratic Functional with a Partly Singular Legendre Condition. Moscow University Comput. Mathematics and Cybernetics, v. 34, no. 1, p. 16–25, 2010.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Wolf
    • 1
    Email author
  • Achim Koberstein
    • 1
  • Tim Hultberg
    • 2
  1. 1.University of PaderbornPaderbornGermany
  2. 2.EumetsatGermany

Personalised recommendations