Advertisement

Stochastic programming methods in systems engineering

  • N. T. Kottegoda

Abstract

The application of optimisation and decision theory in water resource engineering is evidenced by a proliferation of research activities during the past two decades. Originally, such methods were based on a deterministic approach, on the assumption that system inputs are known or could be replaced by their mean values. In recent times, however, the scope and diversity of planning and design has increased. Therefore, the need has arisen for a more flexible methodology, one that can cope, in some practical way, with incomplete information and uncertainty beyond the mean and variance. Nowhere is this more appropriate than in hydrological situations where nature appears to behave in an unpredictable manner.

Keywords

Water Resource Dynamic Programming Water Resource System Reservoir State Geometric Programming 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aron, G., and Scott, V. H. (1971). Dynamic programming for conjunctive water use. J. Hydraul. Div., Am. Soc. Civ. Eng., 97 (HY5), 705–21Google Scholar
  2. Askew, A. J. (1974). Optimum reservoir operating policies and the imposition of a reliability constraint. Water Resour. Res., 10, 51–6CrossRefGoogle Scholar
  3. Askew, A. J.(1975). Use of risk premiums inchance-constrained dynamic pro gramming. Water Resour. Res., 11, 862–6CrossRefGoogle Scholar
  4. Balas, E. (1965). An additional algorithm for solving linear programs with zero-one variables. Oper. Res., 13, 517–46MathSciNetMATHCrossRefGoogle Scholar
  5. Baumol, W. J. (1972). Economic Theory and Operations Analysis, 3rd edn, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  6. Beard, L. R. (1973). Status of water resource systems analysis. J. Hydraul. Div., Am. Soc. Civ. Eng., 99 (HY4), 559–65Google Scholar
  7. Becker, L., and Yeh, W. W. C. (1974). Optimization of real time operation of a multiple-reservoir system. Water Resour. Res., 10, 1107–12CrossRefGoogle Scholar
  8. Bellman, R. E. (1957). Dynamic Programming, Princeton University Press, Princeton, New JerseyMATHGoogle Scholar
  9. Bellman, R. E., and Dreyfus, S. E. (1962). Applied Dynamic Programming, Princeton University Press, Princeton, New JerseyMATHGoogle Scholar
  10. Bellmore, M., and Nemhauser, G. L. (1968). The travelling salesman problem: a survey. Oper. Res., 16, 538–58MathSciNetMATHCrossRefGoogle Scholar
  11. Bishop, A. B., McKee, M., Morgan, T. W., and Narayanan, R. (1976). Multiobjective planning: concepts and methods. J. Water Resour. Plan. Manage. Div., Am. Soc. Civ. Eng., 102 (WR2), 239–53Google Scholar
  12. Buras, N. (1966). Dynamic programming in water resources development. Adv. Hydrosci., 3, 367–412CrossRefGoogle Scholar
  13. Butcher, W. S. (1971). Stochastic dynamic programming for optimum reservoir operation. Water Resour. Bull., 7, 115–23CrossRefGoogle Scholar
  14. Butcher, W. S., Haimes, Y. Y., and Hall, W. A. (1969). Dynamic programming for the optimal sequencing of water supply projects. Water Resour. Res., 5, 1196–204CrossRefGoogle Scholar
  15. Carlson, J. G. H., and Misshauk, M. J. (1972). Introduction to Gaming: Management Decision Simulations, Wiley, New YorkGoogle Scholar
  16. Charnes, A., and Cooper, W. W. (1960). Chance-constrained programming. Manage. Sci., 6, 73–9MathSciNetMATHCrossRefGoogle Scholar
  17. Checkland, P. B. (1970). Systems and science, industry and innovation. J. Syst. Eng., 1, No. 2, 3–17Google Scholar
  18. Churchman, C. W., Ackoff, R. L., and Arnoff, E. L. (1957). Introduction to Operations Research, Wiley, New YorkMATHGoogle Scholar
  19. Cohon, J. L., and Marks, D. H. (1973). Multiobjective screening models and water resource investment. Water Resour. Res., 9, 826–36CrossRefGoogle Scholar
  20. Cole, J. A. (1975). Assessment of surface water sources. Proceedings of the Conference of Engineering Hydrology Today, Institution of Civil Engineers, London, pp. 113–25Google Scholar
  21. Cooper, L., and Steinberg, D. (1970). Introduction to Methods of Optimization, Saunders, Philadelphia, PennsylvaniaMATHGoogle Scholar
  22. Croley, T. E., II (1974). Sequential stochastic optimization for reservoir system. J. Hydraul. Div., Am. Soc. Civ. Eng., 100 (HY1), 201–19Google Scholar
  23. Curry, G. L., Helm, J. C., and Clark, R. A. (1973). Chance-constrained model of system of reservoirs. J. Hydraul. Div., Am. Soc. Civ. Eng., 99 (HY12), 2353–66Google Scholar
  24. Dantzig, G. B. (1963). Linear Programming and Extensions, Princeton University Press, Princeton, New JerseyMATHGoogle Scholar
  25. Deininger, R. A. (1969). Linear programming for hydrologic analyses. Water Resour. Res., 5, 1105–9CrossRefGoogle Scholar
  26. Dorfman, R. (1962). Mathematical models: the multistructure approach. Design of Water Resources Systems (eds A. Maass et al.), Harvard University Press, Cambridge, Massachusetts, chapter 13, pp. 494–539Google Scholar
  27. Dorfman, R. (1965). Formal models in the design of water resource systems. Water Resour. Res., 1, 329–36CrossRefGoogle Scholar
  28. Drobny, N. L. (1971). Linear programming applications in water resources. Water Resour. Bull., 7, 1180–93CrossRefGoogle Scholar
  29. Dudley, N. J., and Burt, O. R. (1973). Stochastic reservoir management and system design for irrigation. Water Resour. Res., 9, 507–22CrossRefGoogle Scholar
  30. Duffin, R. J., Peterson, E. L., and Zener, C. (1967). Geometric Programming, Wiley, New YorkMATHGoogle Scholar
  31. Eastman, J., and ReVelle, C. (1973). Linear decision rule in reservoir management and design, 3, direct capacity determination and intraseasonal constraints. Water Resour. Res., 9, 29–42CrossRefGoogle Scholar
  32. Eisel, L. M. (1970). Comments on `The linear decision rule in reservoir management and design’ by C. ReVelle, E. Joeres and W. Kirby. Water Resour. Res., 6, 1239–41Google Scholar
  33. Eisel, L. M. (1972). Chance constrained reservoir model. Water Resour. Res., 8, 339 — 47CrossRefGoogle Scholar
  34. Encyclopaedia Britannica (1977), vol. 12, 15th edn, William Benton, Chicago, Illinois, p. 1067Google Scholar
  35. Fiering, M. B. (1965). Revitalizing a fertile plan. Water Resour. Res., 1, 41–61CrossRefGoogle Scholar
  36. Fults, D. M., and Hancock, L. F. (1972). Optimum operations model for Shasta—Trinity system. J. Hydraul. Div., Am. Soc. Civ. Eng., 98 (HY9), 1497–514Google Scholar
  37. Gablinger, M., and Loucks, D. P. (1970). Markov models for flow regulation. J. Hydraul. Div., Am. Soc. Civ. Eng., 96 (HY1), 165–81Google Scholar
  38. Garcia, L. L. (1974). Optimization of a three reservoir system by dynamic programming. Proceedings of the 1971 Warsaw Symposium on Mathematical Models in Hydrology, vol. 2, International Association of Scientific Hydrology, Paris, pp. 936–41Google Scholar
  39. Garfinkel, R. S., and Nemhauser, G. L. (1972). Integer Programming, Wiley, New YorkMATHGoogle Scholar
  40. Gottfried, B. S., and Weisman, J. (1973). Introduction of Optimization Theory, Prentice Hall, Englewood Cliffs, New JerseyGoogle Scholar
  41. Gue, R. L., and Thomas, M. E. (1968). Mathematical Methods in Operations Research, Macmillan, New YorkGoogle Scholar
  42. Gundelach, J., and ReVelle, C. (1975). Linear decision rule in reservoir management and design, 5, a general algorithm. Water Resour. Res., 11, 204–7CrossRefGoogle Scholar
  43. Haimes, Y. Y. (1977). Hierarchical Analyses of Water Resources Systems, McGraw-Hill, New YorkGoogle Scholar
  44. Haimes, Y. Y., Hall, W. A., and Freedman, H. T. (1975). Multiobjective Optimization in Water Resources Systems, Elsevier, AmsterdamGoogle Scholar
  45. Hall, W. A., and Buras, N. (1961). The dynamic programming approach to water resources development. J. Geophys. Res., 66, 517–20CrossRefGoogle Scholar
  46. Hall, W. A., Butcher, W. S., and Esogbue, A. (1968). Optimization of the operation of a multi-purpose reservoir. Water Resour. Res., 4, 471–477CrossRefGoogle Scholar
  47. Hall, W. A., and Dracup, J. A. (1970). Water Resources Systems Engineering, McGraw-Hill, New YorkGoogle Scholar
  48. Hall, W. A., and Howell, D. T. (1963). The optimization of single purpose reservoir design with the application of dynamic programming to synthetic hydrology samples. J. Hydrol., 1, 355–63CrossRefGoogle Scholar
  49. Hassitt, A. (1968). Solution of the stochastic programming model of reservoir regulation. IBM Washington Sci. Cent., Wheaton, Md., Rep., No. 320–3506Google Scholar
  50. Hillier, F. S., and Lieberman, G. J. (1974). Operations Research, 2nd edn, Holden Day, San Francisco, CaliforniaMATHGoogle Scholar
  51. Himmelblau, D. M. (1972). Applied Nonlinear Programming, McGraw-Hill, New YorkMATHGoogle Scholar
  52. Hipel, K. W., Ragade, R. K., and Unny, T. C. (1974). Metagame analysis of water resources conflicts. J. Hydraul. Div., Am. Soc. Civ. Eng., 100 (HY10), 1437–55Google Scholar
  53. Howard, R. A. (1960). Dynamic Programming and Markov Processes, Massachusetts Institute of Technology Press, Cambridge, Massachusetts; Wiley, New YorkMATHGoogle Scholar
  54. Hufschmidt, M. M. (1962). Analysis by simulation: examination of response surface. Design of Water Resources Systems (eds A. Maass et al.), Harvard University Press, Cambridge, Massachusetts, chapter 10, pp. 391–442Google Scholar
  55. Hufschmidt, M. M(1965).0Field level planning of water resource systems. Water Resour. Res. 1 147–63CrossRefGoogle Scholar
  56. Jacoby, H. D., and Loucks, D. P. (1972). Combined use of optimization and simulation models in river basin planning. Water Resour. Res., 8, 1401–14CrossRefGoogle Scholar
  57. James, W. (1972). Developing simulation models. Water Resour. Res., 8, 15902Google Scholar
  58. Joeres, E. F., Liebman, J. C., and ReVelle, C. S. (1971). Operating rules for joint operation of raw water sources. Water Resour. Res., 7, 225–35CrossRefGoogle Scholar
  59. Johnson, W. K. (1972). Use of systems analysis in water resource planning. J. Hydraul. Div., Am. Soc. Civ. Eng., 98 (HY9), 1543–56Google Scholar
  60. Jovanovic, S. (1967). Optimization of the long-term operation of a single-purpose reservoir. Proceedings of the International Hydrology Symposium, vol. 1, Fort Collins, Colorado, pp. 422–9Google Scholar
  61. Kall, P. (1976). Stochastic Linear Programming, Springer, BerlinMATHCrossRefGoogle Scholar
  62. Klemeš, V. (1975). Comments on ‘Optimum reservoir operating policies and the imposition of a reliability constraint’ by A. J. Askew. Water Resour. Res., 11, 365–8CrossRefGoogle Scholar
  63. Kos, Z. (1975). Chance constrained model of water resources systems. Proceedings of International Symposium and Workshops on the Application of Mathematical Models in Hydrology and Water Resource Systems, International Association of Scientific Hydrology, Bratislava, preprintsGoogle Scholar
  64. Kramer, N. J. T. A., and de Smit, J. (1977). Systems Thinking, Martinus Nijhoff Social Sciences Division, LeidenCrossRefGoogle Scholar
  65. Kuester, J. L., and Mize, J. H. (1973). Optimization Techniques with FORTRAN, McGraw-Hill, New YorkMATHGoogle Scholar
  66. Lane, M. (1973). Conditional chance-constrained model for reservoir control. Water Resour. Res., 9, 937–48CrossRefGoogle Scholar
  67. Larson, R. E. (1968). State Increment Dynamic Programming, American Elsevier, New YorkMATHGoogle Scholar
  68. Larson, R. E., and Keckler, W. G. (1969). Applications of dynamic programming to the control of water resource systems. Automatica, 5, 15–26CrossRefGoogle Scholar
  69. LeClerc, G., and Marks, D. H. (1973). Determination of the discharge policy for existing reservoir networks under differing objectives. Water Resour. Res., 9, 1155–65CrossRefGoogle Scholar
  70. Lee, E. S., and Waziruddin, S. (1970). Applying gradient projection and conjugate gradient to the optimum operation of reservoirs. Water Resour. Bull., 6, 713–24CrossRefGoogle Scholar
  71. Liebman, J. C., and Lynn, W. R. (1966). Optional allocation of stream dissolved oxygen. Water Resour. Res., 2, 581–91CrossRefGoogle Scholar
  72. Little, J. D. C. (1955). The use of storage water in a hydroelectric system. J. Oper. Res. Soc. Am., 3, 187–97Google Scholar
  73. Liu, C., and Tedrow, A. C. (1973). Multilake river system operation rules. J. Hydraul. Div., Am. Soc. Civ. Eng., 99 (HY9), 1369–81Google Scholar
  74. Loucks, D. P. (1968). Computer models for reservoir regulation. J. Sanit. Eng. Div., Am. Soc. Civ. Eng.,94 (SA4), 657–69Google Scholar
  75. Loucks, D. P. (1970). Some comments on linear decision rules and chance constraints. Water Resour. Res., 6, 668–71CrossRefGoogle Scholar
  76. Loucks, D. P., and Dorfman, P. J. (1975). An evaluation of some linear decision rules in chance-constrained models for reservoir planning and operation. Water Resour. Res., 11, 777–82CrossRefGoogle Scholar
  77. Luthra, S. S., and Arora, S. R. (1976). Optimal design of single reservoir system using δ release policy. Water Resour. Res., 12, 606–12CrossRefGoogle Scholar
  78. Maki, D. P., and Thompson, M. (1973). Mathematical Models and Applications, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  79. Manne, A. S. (1960). Linear programming and sequential decisions. Manage. Sci., 6, 259–67MathSciNetMATHCrossRefGoogle Scholar
  80. Martin, M. J. C., and Denison, R. A. (eds) (1971). Case Exercises in Operations Research, Interscience, Wiley, Chichester, SussexGoogle Scholar
  81. Mawer, P. A., and Thorn, D. (1974). Improved dynamic programming procedures and their practical application to water resource systems. Water Resour. Res., 10, 183–90CrossRefGoogle Scholar
  82. McMillan, C., and Gonzalez, R. F. (1973). Systems Analysis, A Computer Approach to Decision Models, 3rd edn, Irwin, Homewood, IllinoisMATHGoogle Scholar
  83. Mejia, J. M., Egli, P., and LeClerc, A. (1974). Evaluating multireservoir operating rules. Water Resour. Res.,10, 1090–8CrossRefGoogle Scholar
  84. Meredith, D. D., Wong, K. W., Woodhead, R. W., and Workman, R. H. (1973). Design and Planning of Engineering Systems, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  85. Meta Systems Incorporated (1975). Systems analysis in water resources planning. Water Inform. Cent., Port Washington, N.Y., Publ.Google Scholar
  86. Moran, P. A. P. (1970). Simulation and evaluation of complex water systems operations. Water Resour. Res., 6, 1737–42CrossRefGoogle Scholar
  87. Nayak, S. C., and Arora, S. R. (1971). Optimal capacities for a multireservoir system using the linear decision rule. Water Resour. Res., 7, 485–98CrossRefGoogle Scholar
  88. Nayak, S. C., (1974). Linear decision rule: a note on control volume being constant. Water Resour. Res., 10, 637–42CrossRefGoogle Scholar
  89. Nemhauser, G. L. (1966). Introduction to Dynamic Programming, Wiley, New YorkGoogle Scholar
  90. de Neufville, R., and Marks, D. H. (eds) (1974). Systems Planning and Design, Case Studies in Modelling, Optimization and Evaluation, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  91. Norman, J. M. (1972). Heuristic Procedures in Dynamic Programming, Manchester University Press, ManchesterGoogle Scholar
  92. Norman, J. M. (1975). Elementary Dynamic Programming, Edward Arnold, LondonMATHGoogle Scholar
  93. O’Laoghaire, D. T., and Himmelblau, D. M. (1974). Optimal Expansion of a Water Resources System, Academic Press, New YorkMATHGoogle Scholar
  94. Orlob, G. T., and Dendy, B. B. (1973). Systems approach to water quality management. J. Hydraul. Div., Am. Soc. Civ. Eng., 99 (HY4), 573–87Google Scholar
  95. Polya, G. (1957). How to Solve it, Doubleday, New YorkGoogle Scholar
  96. ReVelle, C., and Gundelach, J. (1975). Linear decision rule in reservoir management and design, 4, a rule that minimizes output variance. Water Resour. Res.,11, 197–203CrossRefGoogle Scholar
  97. ReVelle, C., Joeres, E., and Kirby, W. (1969). The linear decision rule in reservoir management and design, 1, development of the stochastic model. Water Resour. Res., 5, 776–7Google Scholar
  98. ReVelle, C., and Kirby, W. (1970). Linear decision rule in reservoir management and design, 2, performance optimization. Water Resour. Res., 6, 1033–44CrossRefGoogle Scholar
  99. Riggs, J. L., and Inoue, M. S. (1976). Introduction to Operations Research and Management Science, McGraw-Hill, New YorkGoogle Scholar
  100. Roefs, T. G. (1968). Reservoir management: the state of the art. IBM Washington Sci. Cent., Wheaton, Md., Rep., No. 320–3508Google Scholar
  101. Roefs, T. G., and Bodin, L. D. (1970). Multireservoir operation studies. Water Resour. Res., 6, 410–20CrossRefGoogle Scholar
  102. Rogers, P. (1969). A game theory approach to the problems of international river basins. Water Resour. Res., 5, 749–60CrossRefGoogle Scholar
  103. Rossman, L. A. (1977). Reliability-constrained dynamic programming and randomized release rules in reservoir management. Water Resour. Res., 13, 247–55CrossRefGoogle Scholar
  104. Rustagi, J. S. (1976). Variational Methods in Statistics, Academic Press, New YorkMATHGoogle Scholar
  105. Schweig, Z. (1968). Reservoir yield, III, optimization of control rules for water storage systems by dynamic programming. Water Res. Assoc., Medmenham, Tech. Paper, No. TP. 61Google Scholar
  106. Schweig, Z., and Cole, J. A. (1968). Optimal control of linked reservoirs. Water Resour. Res., 4, 479–97CrossRefGoogle Scholar
  107. Shamblin, J. E., and Stevens, G. T., Jr. (1974). Operations Research, A Fundamental Approach, McGraw-Hill, New YorkGoogle Scholar
  108. Siddall, J. N. (1972). Analytical Decision Making in Engineering Design, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  109. Silver, R. J., Okun, M. H., and Russell, S.O. (1972). Dynamic programming in a hydroelectric system. Modelling of Water Resources Systems, vol. 2 (ed. A. K. Biswas), Harvest House, Montreal, pp. 623–36Google Scholar
  110. Smith, D. V. (1973). Systems analysis and irrigation planning. J. Irrig. Div., Am. Soc. Civ. Eng., 99 (IRI), 89–107Google Scholar
  111. Sniedovich, M. (1978). On the reliability of reliability constraints. Proceedings of the International Symposium on Risk and Reliability in Water Resources, Waterloo, Canada, 26–28 June 1978 preprintsGoogle Scholar
  112. Sniedovich, M., and Davis, D. R. (1975). Comment on ‘Chance-constrained dynamic programming and optimization of water resource systems’ by A. J. Askew. Water Resour. Res., 11, 1037–8CrossRefGoogle Scholar
  113. Sobel, M. J. (1965). Water quality improvement programming problems. Water Resour. Res., 1, 477–87CrossRefGoogle Scholar
  114. Taha, H. A. (1976). Operations Research, 2nd edn, Macmillan, New YorkMATHGoogle Scholar
  115. Thomas, H. A., Jr., and Watermeyer, P. (1962). Mathematical models: a stochastic sequential approach. Design of Water Resources Systems (eds A. Maass et al.), Harvard University Press, Cambridge, Massachusetts, chapter 14, pp. 540–61Google Scholar
  116. Thuesen, H. G., Fabrycky, W. J., and Thuesen, G. J. (1977). Engineering Economy, 5th edn, Prentice-Hall, Englewood Cliffs, New JerseyGoogle Scholar
  117. Tintner, G., and Sengupta, J. K. (1972). Stochastic Economics, Academic Press, New YorkMATHGoogle Scholar
  118. Wagner, H. M. (1975). Principles of Operations Research, 2nd edn, Prentice-Hall, New YorkGoogle Scholar
  119. White, D., Donaldson, W., and Lawrie, N. (1974). Operation Research Techniques, vol. 2, Business Books, LondonGoogle Scholar
  120. Wilde, D. J., and Beightler, C. S. (1967). Foundations of Optimization, Prentice-Hall, Englewood Cliffs, New JerseyMATHGoogle Scholar
  121. Williams, A. C. (1965). On stochastic linear programming. J. Soc. Ind. Appl. Math., 13, 927–40MathSciNetMATHCrossRefGoogle Scholar
  122. Williams, J. D. (1966). The Compleat Strategyst, revised edn, McGraw-Hill, New YorkGoogle Scholar
  123. Young, G. K. (1967). Finding reservoir operating rules. J. Hydraul. Div., Am. Soc. Civ. Eng., 93 (HY6), 297–321Google Scholar
  124. Zoutendijk, G. (1976). Mathematical Programming Methods, North-Holland, AmsterdamMATHGoogle Scholar

Copyright information

© N. T. Kottegoda 1980

Authors and Affiliations

  • N. T. Kottegoda
    • 1
  1. 1.Department of Civil EngineeringUniversity of BirminghamUK

Personalised recommendations