Skip to main content
SpringerLink
Log in

An approximation scheme for stochastic dynamic optimization problems

  • Chapter
  • First Online:
Stochastic Programming 84 Part I

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 27))

  • 100 Accesses

Abstract

An approximation approach with computable error bounds is derived for a class of stochastic dynamic optimization problems that are too complex to be exactly solvable by straightforward dynamic programming. In particular, a problem arising from oil exploration is considered: for this problem, using the proposed approach, computational results are derived and compared to those obtained by means of other recent approximation schemes.

Partially supported by the Italian Ministry of Education within the project 40% ”Calcolo stocastico e sistemi dinamici stocastici“.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Andreatta, ”Computational problems arising in PPMWOR sampling“, LADSEB-CNR internal report 10/83 (Padova, Italy, 1983).

    Google Scholar 

  2. G. Andreatta and G.M. Kaufman, ”Estimation of finite population properties when sampling is without replacement and proportional to magnitude“, Working paper EL 82-027WP, Energy Laboratory, MIT (Cambridge, MA, 1983).

    Google Scholar 

  3. E. Barouch and G.M. Kaufman, ”Estimation of undiscovered oil and gas“, in: P. Dax, ed., Mathematical aspects of production and distribution of energy, Proceedings of the symposia in applied mathematics, volume XXI, (American Mathematical Society, Providence, R.I., 1977) pp. 77–91.

    Google Scholar 

  4. J. Birge and R.J.-B. Wets, ”Designing approximation schemes for stochastic programs with recourse“, HASA working paper WP-83-111 (Laxenburg, Austria, 1983).

    Google Scholar 

  5. K. Hinderer, ”Foundation of non-stationary, dynamic programming with discrete-time parameter“, Lecture Notes in Operations Research and Mathematical Systems 33 (Springer, Berlin, 1970).

    Google Scholar 

  6. K. Hinderer, ”Estimates for finite-stage dynamic programs“ Journal of Mathematical Analysis and Applications 55 (1976) 207–238.

    Article  MATH  MathSciNet  Google Scholar 

  7. K. Hinderer, ”On approximate solutions of finite-stage dynamic programs“, in: M. Puterman, ed., Dynamic programming and its applications (Academic Press, London, 1979) pp. 289–317.

    Google Scholar 

  8. P. Kall and D. Stoyan, ”Solving stochastic programming problems with recourse including error bounds“, Matematische Operationsforschung und Statistik Series Optimization 13 (1982) 431–447.

    MATH  MathSciNet  Google Scholar 

  9. G.M. Kaufman and J.-W. Wang, ”Model mis-specification and the Princeton study of volume and area of oil fields and their impact on the order of discovery“, Working paper EL-80-003WP, Energy Laboratory, MIT (Cambridge, MA, 1980).

    Google Scholar 

  10. G.M. Kaufman, W. Runggaldier and Z. Livne, ”Predicting the time-rate of supply from a petroleum play“, in: J. B. Ramsey, ed., The economics of exploration for energy resources (JAI Press, Greenwich, CT, 1981) pp. 69–102.

    Google Scholar 

  11. L.K. Platzman, ”Finite-memory estimation and control of finite probabilistic systems“, Ph.D. thesis, MIT, also MIT Report ESL-R-723 (Cambridge, MA, 1977).

    Google Scholar 

  12. U. Rieder, ”Bayesian dynamic programming“, Advances in Applied Probability 7 (1975) 330–348.

    Article  MATH  MathSciNet  Google Scholar 

  13. W.J. Runggaldier and F. Spizzichino, ”Approximations and bounds for a generalized optimal stopping problem“, Zeitschrift für Operations Research 26 (1982) 143–155.

    Article  MATH  MathSciNet  Google Scholar 

  14. R.F. Serfozo, ”Monotone optimal policies for Markov decision processes“, Mathematical Programming Study 6 (1976) 202–215.

    MathSciNet  Google Scholar 

  15. J.L. Smith and G.L. Ward, ”Maximum likelihood estimates of the size distributions of North Sea oil deposits“, Working Paper EL-80-027WP, Energy Laboratory, MIT (Cambridge, MA, 1980).

    Google Scholar 

  16. K.M. van Hee, Bayesian control of Markov chains, Mathematical Centre Tracts 95 (Amsterdam, 1978).

    Google Scholar 

  17. K.H. Waldman, ”On bounds for dynamic programs“, Mathematics of Operations Research (to appear).

    Google Scholar 

  18. W. Whitt, ”Approximations of dynamic programs-I“, Mathematics of Operations Research 3 (1978) 231–243.

    Article  MATH  MathSciNet  Google Scholar 

  19. W. Whitt, ”Approximations of dynamic programs-II“, Mathematics of Operations Research 4 (1979) 179–185.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartmento di Statistica, Università di Padova, I-35100, Padova, Italy

    Giovanni Andreatta

  2. Seminario Matematico, Università di Padova, I-35100, Padova, Italy

    Wolfgang J. Runggaldier

Authors
  1. Giovanni Andreatta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wolfgang J. Runggaldier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Andras Prékopa Roger J.- B. Wets

Rights and permissions

Reprints and permissions

Copyright information

© 1986 The Mathematical Programming Society, Inc.

About this chapter

Cite this chapter

Andreatta, G., Runggaldier, W.J. (1986). An approximation scheme for stochastic dynamic optimization problems. In: Prékopa, A., Wets, R.J.B. (eds) Stochastic Programming 84 Part I. Mathematical Programming Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121116

Download citation

  • DOI: https://doi.org/10.1007/BFb0121116

  • Received:

  • Revised:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00924-2

  • Online ISBN: 978-3-642-00925-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation