Chebyshev Model for Water-Quality Management

A Chebyshev criterion is used to develop robust direct regulation water-quality management models. The reserve capacity of the stream, in terms of the excess capacities above the water-quality goal at the most critical water-quality checkpoints, is used as a measure of robustness of the management solutions to uncertainties in the water-quality input information. The models maximize the minimum reserve capacity along the river. They are applied to the control of biochemical oxygen–demanding waste in an example river basin based on the Willamette River in Oregon. The addition of a robustness measure in the model formulation gives additional insight into the management system. Although the mathematical formulation of the application is simple, the results provide important information for decision makers, such as identifying polluters with high waste-treatment cost per unit dissolved oxygen improvement at the critical stream locations. Such information is often useful for screening alternative options and making sophisticated water-quality policy and management decisions, based on detailed dynamic water-quality simulation.