Improved Dynamic Programming for Reservoir Flood Control Operation

Abstract

In flood control operation, the maximum release from a reservoir is minimized to lessen flood risks. Two properties of the minimax problem are derived by formulating the multi-period decision process as a recursive two-stage model. First, the cost-to-go function, which represents the maximum release in the remaining periods, is a non-decreasing function of the carryover storage. Second, monotonic relationships exist between the initial storage of the two-stage model and the optimal decisions of release and carryover storage. The two properties hold not only in the deterministic case with a given streamflow scenario, but also in the stochastic case with an ensemble of streamflow scenarios. The monotonic relationships are incorporated into the dynamic programming (DP) and sampling stochastic DP (SSDP). Two novel algorithms—improved DP (IDP) and improved SSDP (ISSDP)—are developed. The algorithms are applied to a case study of the Danjiangkou Reservoir in Central China. IDP and ISSDP respectively obtain the same decisions as DP and SSDP, and they are more computationally efficient. The execution times of IDP and ISSDP increase linearly with the number of storage discretizations, while those of DP and SSDP increase quadratically. With 1000 discretizations of reservoir storage, IDP and ISSDP derive optimal decisions at 0.939 and 97.453 s, respectively, whereas DP and SSDP finish at 115.931 and 6372.915 s, respectively. These results suggest that IDP and ISSDP can be useful tools for flood control operation – testing different flood scenarios and determining the optimal decisions.