Skip to main content
SpringerLink
Log in

Optimal operation of a water resources system by stochastic programming

  • Chapter
  • First Online:
Mathematical Programming in Use

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 9))

Abstract

The model concerns the water release and distribution problem of the Karun River and its tributaries in Khuzestan, Iran. The system consists of three dams with three hydroelectric plants, 16 irrigation areas and 13 municipal/industrial demand locations. Water inflows fluctuate with time. A large nonlinear stochastic programming model was formulated to determine the optimal monthly water release rules for the dams for the whole year. Recourse actions and chance constraints are incorporated in the model to account for the uncertainty of the inflows. Detailed water distributions to various sectors are treated as linear programming subproblems.

The original paper has been presented at the Seventh World Congress of International Federation of Automatic Control, Helsinki. June 12–16, 1978. The copyright of the paper has been released by IFAC.

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. P.A.P. Moran, “A probability theory of a dam with a continuous release”, Quarterly J. of Mathematics 7 (1956) 130.

    Article  MATH  Google Scholar 

  2. M.B. Fiering, “Queuing theory and simulation in reservoir design”, J. of Hydraul. Div. Amer. Soc. Civil. Engr. 87 (1961) 39.

    Google Scholar 

  3. H.A. Thomas, Jr. and M.B. Fiering, “Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation”, in: A. Maass et al., eds., Design of water resources systems (Harvard University Press, Cambridge, MA, 1962) Ch. 12, pp. 459–493.

    Google Scholar 

  4. M.M. Hufschmidt and M.B. Fiering, Simulation techniques for design of water resources systems (Harvard University Press, Cambridge, MA, 1962).

    Google Scholar 

  5. A.S. Manne, “Linear programming and synthesis decisions”, Management Science 6 (1960) 259.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Dorfman, R., “Mathematical models: The multi-structure approach”, in: A. Maass et al., eds., Design of water resources systems (Harvard University Press, Cambridge, MA, 1962), Ch. 12, pp. 494–539.

    Google Scholar 

  7. H.A. Thomas and P. Watermeyer, “Mathematical models: A stochastic sequential approach”, in: A. maass et al., Design of water resources systems (Harvard University Press, Cambridge, MA, 1962), Ch. 14, pp. 540–561.

    Google Scholar 

  8. P. Masse. Les reserves et la regulation de l’avenir dans la vie economique, Vol. 2 (Herman, Paris, 1946).

    Google Scholar 

  9. J.D.C. Little, “The use of storage water in a hydroelectric system”, Operations Research 3 (1955) 187.

    Article  Google Scholar 

  10. W.A. Hall and N. Buras, “The dynamic programming approach to water resources development”, J. of Geophys. Res. 66 (1961) 517.

    Article  Google Scholar 

  11. W.A. Hall and D.T. Howell, “The optimization of single-purpose reservoir design with the application of dynamic programming to synthetic hydrology samples”, J. Hydrol. 1 (1963) 355.

    Article  Google Scholar 

  12. G.K. Young, Jr., “Finding reservoir operating rules”, J. Hydraul. Div. Amer. Soc. Civil Engr. 93 (1967) 297.

    Google Scholar 

  13. Z. Schweig and J.A. Cole, “Optimal control of linked reservoirs”, Water Resources Research 4 (3) (1968) 479–497.

    Article  Google Scholar 

  14. R.E. Larson and W.G. Keckler, “Applications of dynamic programming to the control of water resources systems”, JFAC J. Automatica 5 (1969) 15–26.

    Article  Google Scholar 

  15. M. Heidari, V.T. Chow, P.V. Kokotovic and D.D. Meredith, “Discrete differential dynamic programming approach to water resources optimization”, Water Resources Res. 7 (1971) 273.

    Article  Google Scholar 

  16. M. Jamshidi, “Optimization of water resources systems with statistical inflows”, Proceedings of Inst. Elec. Engr. 124 (1977) 79–82.

    Google Scholar 

  17. K. Takeuchi and D.H. Moreau, “Optimal control of multiunit interbasin water resource systems”, Water Resources Research 10 (1974) 407–414.

    Article  Google Scholar 

  18. C. ReVelle, E. Joeres and W. Kirby, “The linear decision rule in reservoir management and design 1: Development of the stochastic model”, Water Resources Research 5 (1969) 767–777.

    Article  Google Scholar 

  19. D.P. Loucks, “Some comments on linear decision rules and chance-constraints”, Water Resources Research 6 (1970) 668.

    Article  Google Scholar 

  20. Harza Engineering Company, The Initial Karun River Project Feasibility Report, I—Project Summary, Chicago, IL (1968).

    Google Scholar 

  21. Harza Engineering Company, Marun River Development Feasibility Report, I, II, III, Chicago, IL (1967).

    Google Scholar 

  22. S.J. Garstka and R.J.B. Wets, “On decision rules in stochastic programming”, Mathematical Programming 7 (1974) 117–143.

    Article  MATH  MathSciNet  Google Scholar 

  23. J. Eastman and C. ReVelle, “Linear decision rule in reservoir management and design 3., direct capacity determination and intraseasonal constraints”, Water Resources Research 9 (1) (1973).

    Google Scholar 

    Google Scholar 

  24. N.J. Dudley and O.R. Burt, “Stochastic reservoir management and system design for irrigation”, Water Resources Research 9 (3) (1973) 507–522.

    Article  Google Scholar 

  25. C. ReVelle and J. Gundelach, “Linear decision rule in reservoir management and design 4, a rule that minimizes output variance”, Water Resources Research 11 (2) (1975) 197–203.

    Article  Google Scholar 

  26. D.P. Loucks and P.J. Dorfman, “An evaluation of some linear decision rules in chanceconstrained models for reservoir planning and operations”, Water Resources Research 11 (6) (1975) 777–782.

    Article  Google Scholar 

  27. A. Charnas and W.W. Cooper, “Deterministic equivalents for optimizing and satisfying under chance-constraints”, Operations Research 8 (1) (1963) 10–39.

    Google Scholar 

  28. G.H. Symonds, “Chance-constrained equivalents of some stochastic programming problems”, Operations Research 16 (2): (1968).

    Google Scholar 

    Google Scholar 

  29. A. Prekopa, “Optimal control of a storage level using stochastic programming”, Problems of Control and Information Theory 4 (3): (1975) 193–204.

    MATH  MathSciNet  Google Scholar 

  30. A. Prekopa, “Stochastic programming for inventory control and water storage problems”, in: A. Prekopa ed., Inventory control and water storage, Colloquia Mathematica Societatis Janos Bolyai 7 (North-Holland, Amsterdam, 1973).

    Google Scholar 

  31. A. Prekopa, “On probabilistic constrained programming”, Princeton symposium on mathematical programming (1970).

    Google Scholar 

  32. R.J.B. Wets, “Programming under uncertainty: the complete problem”, Z. Wahrscheinlichkeitstheorie verw. Geb. 4 (1966) 316–339.

    Article  MATH  MathSciNet  Google Scholar 

  33. R.J.B. Wets, “Stochastic programs with fixed recourse: the equivalent deterministic problems”, SIAM Review 16(13) (1974).

    Google Scholar 

    Google Scholar 

  34. H. Noltemeier, ed., Sensitivitatsanalyse bei diskreten linearen Optimierungsproblemen (Springer, Berlin, 1970).

    Google Scholar 

  35. I.B.M., Mathematical Programming System Extended (MPSX) Primer, Publication No. GH19-1091-0, Paris, France (1974).

    Google Scholar 

  36. I.B.M. Mathematical Programming System Extended (MPSX); Linear and Separable Programming Program Description, Publication No. SH20-0968-0, Program Product Center, Paris, France (1971).

    Google Scholar 

  37. M.J. Hopper, Harwall Subroutine Library, Theoretical Physics, Division, U.K.A.E.A. Research Group, Atomic Energy Research Establishment, AERE-R.7477, Harwell, England (July (1973).

    Google Scholar 

  38. R. Fletcher, “An ideal penalty function for constrained optimization”, C.S.S. 2 (1973).

    Google Scholar 

Download references

Author information

Author notes

  1. Robert J. Peters

    Present address: Institute of Economic Research, University of Groningen, Groningen, the Netherlands

  2. Mohammad Jamshidi

    Present address: Department of Electrical Engineering, Pahlavi University, Shiraz, Iran

Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, U.S.A.

    Robert J. Peters, Kai-Ching Chu & Mohammad Jamshidi

Authors
  1. Robert J. Peters
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai-Ching Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Jamshidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. L. Balinski C. Lemarechal

Rights and permissions

Reprints and permissions

Copyright information

© 1978 The Mathematical Programming Society

About this chapter

Cite this chapter

Peters, R.J., Chu, KC., Jamshidi, M. (1978). Optimal operation of a water resources system by stochastic programming. In: Balinski, M.L., Lemarechal, C. (eds) Mathematical Programming in Use. Mathematical Programming Studies, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120832

Download citation

  • DOI: https://doi.org/10.1007/BFb0120832

  • Received:

  • Revised:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00795-8

  • Online ISBN: 978-3-642-00796-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation