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Modeling Multi-Stage Decision Optimization Problems

  • Ronald Hochreiter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 682)

Abstract

Multi-stage optimization under uncertainty techniques can be used to solve long-term management problems. Although many optimization modeling language extensions as well as computational environments have been proposed, the acceptance of this technique is generally low, due to the inherent complexity of the modeling and solution process. In this paper a simplification to annotate multi-stage decision problems under uncertainty is presented—this simplification contrasts with the common approach to create an extension on top of an existing optimization modeling language. This leads to the definition of meta models, which can be instanced in various programming languages. An example using the statistical computing language R is shown.

References

  1. 1.
    Colombo, M., Grothey, A., Hogg, J., Woodsend, K., Gondzio, J.: A structure-conveying modelling language for mathematical and stochastic programming. Math. Program. Comput. 1(4), 223–247 (2009)CrossRefGoogle Scholar
  2. 2.
    Fourer, R., Gay, D., Kernighan, B.: AMPL: A Modeling Language for Mathematical Programming, 2nd edn. Duxbury/Brooks/Cole Publishing Company, Boston (2002)Google Scholar
  3. 3.
    Heitsch, H., Römisch, W., Strugarek, C.: Stability of multistage stochastic programs. SIAM J. Optim. 17(2), 511–525 (2006)CrossRefGoogle Scholar
  4. 4.
    King, A., Wallace, S.: Modeling with Stochastic Programming. Springer Series in Operations Research and Financial Engineering. Springer, New York (2013)Google Scholar
  5. 5.
    Koch, T.: Rapid mathematical prototyping. Ph.D. thesis, Technische Universität Berlin (2004)Google Scholar
  6. 6.
    Kuhn, D., Wiesemann, W., Georghiou, A.: Primal and dual linear decision rules in stochastic and robust optimization. Math. Program. 130(1), 177–209 (2011)CrossRefGoogle Scholar
  7. 7.
    Lopes, L.B.: Modeling stochastic optimization: from idea to instance. Ph.D. thesis, Northwestern University (2003)Google Scholar
  8. 8.
    R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2013). http://www.R-project.org
  9. 9.
    Ruszczyński, A., Shapiro, A. (eds.): Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10. Elsevier, Amsterdam (2003)Google Scholar
  10. 10.
    Thénié, J., Delft, C.V., Vial, J.P.: Automatic formulation of stochastic programs via an algebraic modeling language. Comput. Manag. Sci. 4(1), 17–40 (2007)CrossRefGoogle Scholar
  11. 11.
    Valente, C., Mitra, G., Sadki, M., Fourer, R.: Extending algebraic modelling languages for stochastic programming. INFORMS J. Comput. 21(1), 107–122 (2009)CrossRefGoogle Scholar
  12. 12.
    van Delft, C., Vial, J.P.: A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains. Automatica 40(5), 743–756 (2004)CrossRefGoogle Scholar
  13. 13.
    Wallace, S.W., Ziemba, W.T. (eds.): Applications of stochastic programming. MPS/SIAM Series on Optimization, vol. 5. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Finance, Accounting and StatisticsWU Vienna University of Economics and BusinessViennaAustria

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