A stochastic dynamic programing model for determining reservoir release rules which maximize expected net benefits subject to reliability constraints on system performance is presented within the framework of Lagrangian duality theory. The approach characterizes optimal release rules under discounting of benefits as being nonstationary. It also indicates when there exists a randomized rule which dominates the optimal deterministic rule. The methodology for obtaining these rules uses dual optimization to provide bounds on the optimal solution and a branch and bound procedure to resolve any duality gap which may occur if the bounds are not equal. The model is applied to a group of hypothetical problems for which nonoptimal policies had previously been found by using chance-constrained dynamic programing (Askew, 1974b).
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