Skip to main content

The Aggregation Principle in Scenario Analysis and Stochastic Optimization

  • Conference paper

Part of the book series: NATO ASI Series ((NATO ASI F,volume 51))

Abstract

Most systems that need to be controlled or analyzed involve some level of uncertainty about the value to assign to some of the parameters, if not about the actual layout of certain subcomponents of the system. In many situations not much is lost by assigning “reasonable” values to these parameters or by choosing a particular design. In other instances ignoring uncertainty may very well lead to totally misleading solutions that would invalidate any of the implications one may wish to draw from the analysis.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Back, Kerry and Stanley Pliska, “The shadow price of information in continuous time decision problems”, Stochastics 22(1987), 151–168.

    Article  MathSciNet  MATH  Google Scholar 

  2. Dempster, Michael, “On stochastic programming: II, Dynamic problems under risk”, Research Report DAL TR 86-5, Dalhousie University, July 1985 (revised June 1986).

    Google Scholar 

  3. Evstigneev, Igor V., “Prices on information and stochastic insurance models”, IIASA CP-85-23 (Laxenburg), April 1985.

    Google Scholar 

  4. Mulvey, John and Hercules Vladimirou, Solving multistage investment problems: an application of scenario aggregation, Statistics and Operations Research SOR 88-1, Princeton University, 1988. Mulvey, John and Hercules Vladimirou, Solving multistage stochastic networks: an application of scenario aggregation, Statistics and Operations Report SOR 88-2, Princeton University, 1988.

    Google Scholar 

  5. Robinson, Stephen M. and Roger J-B Wets, “Stability in two-stage stochastic programming”, SIAM J. on Control and Optimization 25(1987), 1409–1416.

    Article  MathSciNet  MATH  Google Scholar 

  6. Rockafellar, R.T. and Roger J-B Wets, “Stochastic Convex Programming: Kuhn-Tucker Conditions”, J. Mathematical Economics 2(1975), 349–370.

    Article  MathSciNet  MATH  Google Scholar 

  7. Rockafellar, R.T. and Roger J-B Wets, “Nonanticipativity and ℒ1-Martingales in Stochastic Optimization Problems”, Mathematical Programming Study 6(1976), 170–187. Also in: Stochastic Systems: Modeling, Identification and Optimization, R. Wets (ed.), North-Holland, Amsterdam, 1976.

    Article  MathSciNet  Google Scholar 

  8. Rockafellar, R.T. and Roger J-B Wets, “Scenario and policy aggregation in optimization under uncertainty”, IIASA Working Paper WP-87-119, Laxenburg, Austria, December 1987.

    Google Scholar 

  9. Wets, Roger J-B, Large-scale linear programming techniques in stochastic programming, in Numerical Methods for Stochastic Optimization, eds. Y. Ermoliev and R. Wets, Springer Verlag, Berlin, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wets, R.JB. (1989). The Aggregation Principle in Scenario Analysis and Stochastic Optimization. In: Wallace, S.W. (eds) Algorithms and Model Formulations in Mathematical Programming. NATO ASI Series, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83724-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83724-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83726-5

  • Online ISBN: 978-3-642-83724-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics