Skip to main content
Log in

SDDP for multistage stochastic programs: preprocessing via scenario reduction

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

Even with recent enhancements, computation times for large-scale multistage problems with risk-averse objective functions can be very long. Therefore, preprocessing via scenario reduction could be considered as a way to significantly improve the overall performance. Stage-wise backward reduction of single scenarios applied to a fixed branching structure of the tree is a promising tool for efficient algorithms like stochastic dual dynamic programming. We provide computational results which show an acceptable precision of the results for the reduced problem and a substantial decrease of the total computation time.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Bally V, Pages G (2003) Quantization algorithm for solving multidimensional discrete-time optimal stopping problems. Bernoulli 9:1003–1049

    Article  Google Scholar 

  • Bayraksan G, Morton DP (2009) Assessing solution quality in stochastic programs via sampling. In: Oskoorouchi M, Gray P, Greenberg H (eds) Tutorials in operations research. Informs, Hannover, pp 102–122, ISBN 978-1-877640-24-7

  • Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming: an approach using probability metrics. Math Prog 95:493–511

    Article  Google Scholar 

  • Dupačová J, Kozmík V (2015) Structure of risk-averse multistage stochastic programs. OR Spectr 37:559–582

    Article  Google Scholar 

  • Eichhorn A, Römisch W (2005) Polyhedral risk measures in stochastic programming. SIAM J Optim 16:69–95

    Article  Google Scholar 

  • Heitsch H, Römisch W, Strugarek C (2006) Stability of multistage stochastic programs. SIAM J Optim 17:511–525

    Article  Google Scholar 

  • Heitsch H, Römisch W (2009) Scenario tree reduction for multistage stochastic programs. Comput Manag Sci 6:117–133

    Article  Google Scholar 

  • Heitsch H, Römisch W (2009) Scenario tree modeling for multistage stochastic programs. Math Progr 118:371–406

    Article  Google Scholar 

  • Infanger G, Morton DP (1996) Cut sharing for multistage stochastic linear programs with interstage dependency. Math Progr 75:241–256

    Google Scholar 

  • Kozmík V, Morton D (2015) Evaluating policies in risk-averse multi-stage stochastic programming. Math Progr 152:275–300

    Article  Google Scholar 

  • Löhndorf N, Wozabal D, Minner S (2013) Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming. Oper Res 61:810–823

    Article  Google Scholar 

  • Oliveira WL, Sagastizábal C, Penna DDJ, Maceira MEP, Damázio JM (2010) Optimal scenario tree reduction for stochastic streamflows in power generation planning problems. Optim Methods Softw 25:917–936

    Article  Google Scholar 

  • Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math Progr 52:359–375

    Article  Google Scholar 

  • Pflug GCh, Pichler A (2012) A distance for multistage stochastic optimization models. SIAM J Optim 22:1–23

    Article  Google Scholar 

  • Pflug GCh, Pichler A (2011) Approximations for probability distributions and stochastic optimization problems. In: Bertocchi M, Consigli G, Dempster MAH (eds) Stochastic optimization methods in finance and energy. Springer, New York, pp 343–388, ISBN 978-1-4419-9585-8

  • Philpott AB, de Matos VL (2012) Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. Eur J Oper Res 218:470–483

    Article  Google Scholar 

  • Rockafellar RT, Uryasev S (2002) Conditional value at risk for general loss distributions. J Bank Financ 26:1443–1471

    Article  Google Scholar 

  • Römisch W (2003) Stability of stochastic programming problems, Chapter 8. In: Ruszczyński A, Shapiro A (eds) Handbook on stochastic programming. Elsevier, Amsterdam, pp 483–554

    Chapter  Google Scholar 

  • Römisch W (2009) Scenario reduction techniques in stochastic programming. In: Watanabe O, Zeugmann T (eds) Stochastic algorithms: foundations and applications, vol 5792., Lecture notes in computer science. Springer, Sapporo, pp 1–14

  • Shapiro A (2011) Analysis of stochastic dual dynamic programming method. Eur J Oper Res 209:63–72

    Article  Google Scholar 

  • Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on stochastic programming: modeling and theory. SIAM Society for Industrial and Applied Mathematics, Philadelphia, ISBN 978-1107025127

  • Wozabal D (2012) A framework for optimization under ambiguity. Ann Oper Res 193:21–47

    Article  Google Scholar 

Download references

Acknowledgments

Jitka Dupačová has initiated this project and we have worked together till the very final form of the article, unfortunately, she passed away during the publication process. I would like to dedicate this paper to Jitka, for her restless guidance, knowledge, patience and care. The research was partly supported by the project of the Czech Science Foundation P/402/12/G097 ’DYME/Dynamic Models in Economics’.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Václav Kozmík.

Additional information

Jitka Dupačová: Passed away 4 January 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dupačová, J., Kozmík, V. SDDP for multistage stochastic programs: preprocessing via scenario reduction. Comput Manag Sci 14, 67–80 (2017). https://doi.org/10.1007/s10287-016-0261-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10287-016-0261-6

Keywords

Mathematics Subject Classification

Navigation