An Application of Mathematical Programming in Planning Surface Water Storage1

ABSTRACT Designing a surface reservoir involves the concept of reservoir yield. This concept embodies three basic information items: hydrologic regime, active storage volume, and reservoir release policy. In the actual case presented below, the magnitude of the active storage was prescribed by a legal procedure, so that the planning issue became that of determining the reservoir yield given the hydrological information. A stochastic dynamic programming model was formulated to derive a schedule of seasonal optimal reservoir releases and their respective probabilities of occurrence. This schedule is the reservoir yield. The yearly cycle was divided into three seasons representing the actual climatic conditions, and conditional probabilities linking streamflows in consecutive seasons were estimated. An operating policy was postulated, based on the same set of legal decisions that prescribed the active storage volume, and target reservoir releases were assumed. Similarly, target storages at the end of each season were set up. The optimizing/ minimizing criterion in the dynamic programming formulation was the sum of squares of deviations of actual releases and final storage volumes from their respective targets.