Integrating economic and hydrologic interdependence in reservoir management

The purpose of this study is to determine the optimal allocation of reservoir water among competing uses (hydroelectric power generation, lake recreation and urban and rural water supply). An optimization model using nonlinear programming is developed to optimally allocate reservoir water among these uses. It is not unusual to optimize the values for flood control, hydroelectric generation, and urban and rural water uses, and to determine recreation values as a residual. Furthermore, if recreation values are considered, it may be in the form of constraints that maintain reservoir water levels within a specified range. In contrast, this study develops a model in which the recreational benefits depend explicitly on lake water levels, while the flood control capacity of the reservoir is maintained through upper bounds on the lake level. A mass balance equation is used to determine the water levels and volumes in the lake for each month over a twelve‐month period. The General Algebraic Modeling System with MINOS is used to solve this model. The results indicate that the total economic benefits for Lake Tenkiller could be increased by directly including recreational values in the model, and maintaining lake water levels at near‐normal levels that maximize the number of summer visitations. The optimal allocation of Lake Tenkiller water among competing uses also satisfies the equimarginal principle. That is, the marginal value of water at the lake in each month is the same for the last unit of water used for hydroelectric, recreational, or urban and rural water uses. Use of this type of modelling framework would assist policymakers or reservoir managers in reallocation of reservoir water and in calibrating several policy scenarios.