• ON THE THEORY AND MODELING OF DYNAMIC PROGRAMMING WITH APPLICATIONS IN RESERVOIR OPERATION

      Sniedovich, Moshe; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1976-12)
      This dissertation contains a discussion concerning the validity of the principle of optimality and the dynamic programming algorithm in the context of discrete time and state multistage decision processes. The multistage decision model developed for the purpose of the investigation is of a general structure, especially as far as the reward function is concerned. The validity of the dynamic programming algorithm as a solution method is investigated and results are obtained for a rather wide class of decision processes. The intimate relationship between the principle and the algorithm is investigated and certain important conclusions are derived. In addition to the theoretical considerations involved in the implementation of the dynamic programming algorithm, some modeling and computational aspects are also investigated. It is demonstrated that the multistage decision model and the dynamic programming algorithm as defined in this study provide a solid framework for handling a wide class of multistage decision processes. The flexibility of the dynamic programming algorithm as a solution procedure for nonroutine reservoir control problems is demonstrated by two examples, one of which is a reliability problem. To the best of the author's knowledge, many of the theoretical derivations presented in this study, especially those concerning the relation between the principle of optimality and the dynamic programming algorithm, are novel.
    • Preference Criterion and Group Utility Model for Reservoir Control Under Uncertainty

      Krzysztofowicz, Roman (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1978-03)
      From the standpoint of real -time reservoir operation, the multipurpose control problem may be reduced to a dual purpose problem of (1) flood control under uncertain inflow and (2) conservation control (water supply, power generation, low flow augmentation, recreation, etc.) after the flood has receded. A preference criterion for real -time flood control under the conditions of uncertainty is developed in accordance with three postulates: (1) The input to the control process is a probabilistic forecast of the inflow hydrograph, (2) The control decisions are based upon the decision maker's value judgments concerning preferences over operating attributes, trade -offs between reservóir purposes, and attitude toward risk. (3) The conservation control is imbedded into the flood control through the attribute space of the preference criterion allowing thus for explicit consideration of the trade -offs between reservoir purposes. The preference criterion is developed within the framework of utility theory. The value judgments of the decision maker are quantified in terms of a two -attribute disutility function. It is argued that minimization of expected disutility is a plausible and well motivated criterion for multipurpose real -time reservoir control under uncertainty. A suitable disutility model is developed. The case of a group decision maker is analyzed in depth. Common group utility models based on aggregation of individual utility functions and interpersonal utility comparisons are critically reviewed. An alternative approach based on direct group value judgments is suggested, and a general group utility model for decision -making in engineering systems is developed. The disutility assessment procedures are analysed, and response biases that may be introduced into the decision maker's preference structure by the use of an inappropriate assessment scheme are identified. Some principles and novel techniques for assessing disutility functions are advocated; they are motivated by results of psychological research in human decision behavior, and are further supported by experimental evidence. Results of assessment of the reservoir control disutility function for several single and group decision makers are presented.
    • Preferential Reservoir Control Under Uncertainty

      Krzysztofowicz, Roman (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1978-11)
      A model for real -time control of a multipurpose reservoir under the conditions of uncertainty is developed. The control model is formulated as a multistage decision process. It is conceptualized in the form of two sub -processes. The first level process is a Forecast - Strategy Process which performs as an open-loop feedback controller. It is defined by a sequence of forecasts and optimal release strategies against these forecasts. At each forecast time (time of issuing the forecast), the optimal release strategy is computed for the time period equal to the lead time of the forecast, and it remains in execution until the next forecast time. The second level process, defined for each forecast time, is a Control Process which for the given forecast generates the release strategy satisfying the preference criterion (minimization of expected disutility). This process is formulated as a truncated Markovian adaptive controller performing on a finite set of discrete times --the same set which indexes the forecast inflow process. To evaluate the past performance of the control, a set of measures of effectiveness is proposed. Computational aspects of the control model are analyzed. Structural properties of the reservoir control process are explored in the main theorem which assures the monotonicity of the optimal strategy with respect to one of the state variables. Also, the properties of the optimal strategy for the case of a categorical forecast are proven. Next, two suboptimal strategies are derived: (1) partial open -loop strategy and (2) naive /partial open-loop strategy. Finally, a'discretization procedure which guarantees convergence of the numerical solution is discussed, and the computational requirements of the optimal and two suboptimal strategies are compared.