Limitations of deterministic optimization applied to reservoir operations

Deterministic optimization can produce suboptimal reservoir-control policies by failing to incorporate adequately the impact of low-probability events. Resulting operating policies may not efficiently balance the costs of rationing, minor flooding, or other short-term impacts with the severe impacts of extreme flood or drought. This occurs when deterministic optimization is applied to systems that are not "certainty equivalent." This paper demonstrates this by contrasting control policies developed using deterministic optimization of inflow forecasts with control policies using stochastic optimization of probabilistic inflows. For a range of hypothetical reservoir-control problems, it is observed that deterministic optimization results in costs that are greater on average and that are much greater for extreme events, particularly for reservoir systems with limited storage capacity and for objectives described by nonquadratic functions. This is true even when forecasts are relatively accurate, such as when streamflows are highly autocorrelated.