Capacity decisions in a multipurpose multireservoir system

Abstract

A mathematical programing model is proposed to solve the common and formidable water resource planning problem of finding the best sites from a number of potential sites for constructing a system of reservoirs that will optimally meet the various water demands. Since flood damages and shortage costs (the primary problems the reservoirs are designed to solve) usually vary nonlinearly with the flow values, a nonlinear programing model is proposed. The fact that the variables in the objective function, which minimizes the sum of the annual amortized cost of the reservoirs and the annual flood and shortage losses less the annual recreational benefits, and the variables in the constraints are separable has been used to reduce the nonlinear problem to a separable problem. The common approximate approach to the problem, which chooses the optimal design parameters on the basis of straight historical inflow data for a specified period, was selected over the more complex ideal approach, which quantifies the stochastic nature of the historical inflows and uses the inflow distributions in an optimization model to select the design parameters. The optimization in this paper considers the flood inflows (based on a given flood frequency) and the drought inflows (based on the severest drought on record) simultaneously. The damages due to shortages may be weighted further in the objective function. The present model differs from other models in that releases are constrained only by the availability of water and their optimal values are determined by balancing damages downstream against the cost of providing storage to prevent them. The model is applied to U.S. Army Corps of Engineers data for the Minnesota River basin, and the results are compared with the plan proposed by the Corps.