Stochastic Dynamic System Theory: A Challenge for Natural Resources Management

  • Eric Parent
Part of the NATO ASI Series book series (volume 29)


Most of stochastic modeling methods in natural resources are based on a set of analytical model equations, mainly transport and mass-balance equations including stochastic behavior of model variables. These techniques belong to system analysis and control theory and they have become a common practice in engineering studies although the decision making implications and limits of such models are not often explicitly realized. This paper gives a general overview of sequential optimization and system analysis applied to the field of water resource and environmental engineering. It underlines the advantages but also the limits and the weak points of such an approach especially with regards to risk management and multicriterion decision making.


Dynamic Programming Optimal Policy Natural Resource Management Reward Function Water Resource Research 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alexéev V., Galéev E., Tikhomirov V. (1987), Recueil de problemes d’optimisation, Editions Mir.Google Scholar
  2. Arnold L. (1974), Stochastic differential equations: Theory and applications. Wiley.Google Scholar
  3. Askew J.A. (1974), Optimum reservoir operating policies and the imposition of a reliability constraint. Water resources research 10, 1, p.51–56CrossRefGoogle Scholar
  4. Bellman R.E. (1957), Dynamic programming. Princeton University pressGoogle Scholar
  5. Beltrami E. (1987), Mathematics for dynamic modeling. Academic PressGoogle Scholar
  6. Denardo E.V. (1982), Dynamic programming. Prentice HallGoogle Scholar
  7. Duckstein L., Plate E.J. and Benedini M. (1987), A System framework in “Engineering reliability and risk in water resources “(Duckstein & Plate), Dordrec htGoogle Scholar
  8. Faurre P, Robin M. (1984), Elements d’automatique. DunodGoogle Scholar
  9. Foufoula-Georgiou E. and Kitanidis P. (1988), Gradient dynamic programming for stochastic optimum control of multidimensional water resources systems. Water resources researchGoogle Scholar
  10. Friedland B. (1986), Control system design. McGraw-Hill, NYGoogle Scholar
  11. Gal S. (1979), Optimal management of a multireservoir water system, Water resources research 15, p.737–749CrossRefGoogle Scholar
  12. Hashimoto T., Stedinger J.R. and Loucks D.P. (1982), Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water resources research 18, 1, p. 14–20CrossRefGoogle Scholar
  13. Henig M. (1985), The shortest path problems with two objective function, European J. of operation research 25, p.281–291.CrossRefGoogle Scholar
  14. Jacobson D. and Mayne D. (1970), Differential dynamic programming. American Elsevier Cie.Google Scholar
  15. Karlsson P. and Haimes Y. (1988), Probability and their partitioning. Water resources research 24, 1, p.21–29CrossRefGoogle Scholar
  16. Kitanidis P.K. (1987), A first order approximation to stochastic optimum control of reservoirs, stochastic hydro hydraul., p. 169–182Google Scholar
  17. Klemes V. (1977), Discrete representation of storage for stochastic reservoir optimization. Water resources research 13, 1, p.l49—158CrossRefGoogle Scholar
  18. Klemes V. (1978), The unreliability of reliability estimates of storage reservoir performance based on short streamflow records. In “Water resource management, Water Resource Publications, Fort Collins, Colorado”, p. 193–205Google Scholar
  19. Kree P. and Soize C. (1983), Mecanique aleatoire. BordasGoogle Scholar
  20. Krzysztofowicz R. (1982), Utility criterion for water supply: Quantifying value of water and risk attitude. In “Decision-making for hydrosystems-Forecasting and operation” (T. Unny), 43–62Google Scholar
  21. Li D. and Haimes Y. (1987), Risk management in a hierarchical multiobjective framework. In “Towards interactive and intelligent decision support system” (eds. Y Sawaragi, K. Inoue and H. Nakayama) Springer VerlagGoogle Scholar
  22. Masse P. (1959), Le choix des investissements. DunodGoogle Scholar
  23. Mitten L. (1974), Preference order Dp., Management science 21, p.43–46CrossRefGoogle Scholar
  24. Parent E., Lebdi F. and Hurand P. (1991), Gestion strategique du systeme Neste. to appear in Revue des sciences de l’eauGoogle Scholar
  25. Saad M. and Turgeon A. (1988), Application of principal component analysis to long term reservoir management, Water resources research 7, 1Google Scholar
  26. Simonovic S.P. and Orlob T.G. (1984), Risk-reliability programming for optimal water quality control. Water resources research 20, 6, p.639–646CrossRefGoogle Scholar
  27. Sniedovith M. (1986), A new look at Bellman Principe of optimality, Journal of optimization theory and optimizationGoogle Scholar
  28. Tapiero C.S. (1988), Applied stochastic models & control in management. In “Advanced series in management”, V12. North-HollandGoogle Scholar
  29. Turgeon A. (1980), Optimal operation of multireservoir power systems with stochastic inflow. Water resources research 16, 2, p.275–283CrossRefGoogle Scholar
  30. Turgeon A. (1981), Optimal short term hydro scheduling from the principle of progressive optimality. Water resources research 17, 3, p.481–486CrossRefGoogle Scholar
  31. Yakowitz S. (1982), Dynamic programming applications in water resources. Water resources research 18, 4, p.673–696CrossRefGoogle Scholar
  32. Yeh W.W.G. (1985), Reservoir management and operations models: A state-of-the-art review. Water resources research 21, 12, p.1797–1818CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Eric Parent
    • 1
  1. 1.Department of Applied Mathematics and Computer ScienceENGREFParisFrance

Personalised recommendations