We propose a simple but non-trivial mathematical model of a dam–reservoir system balancing between the downstream environmental management and hydropower production. We consider a stochastic control problem of the system to find its balanced operation policy. We point out that finding the optimal policy reduces to solving a nonlinear degenerate elliptic equation. This equation is exactly solvable in a reduced case without hydropower production, while it requires numerical computation in more complicated cases. A demonstrative application example with a high-resolution finite difference scheme is finally presented.
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