Linear programming is applied to the management of water quality in a river basin. The charge is to select the efficiencies of the treatment plants on the river that will achieve the dissolved oxygen standards at a minimum cost. The objective function is structured in terms of the costs of the treatment plants. The principal constraints prevent violation of the dissolved oxygen standards. A simplified version of the Willamette River in Oregon is studied, using the linear programming formulation, and the results are compared with those obtained by dynamic programming. The effects of changes in the dissolved oxygen standards are explored by use of the dual variables.
A dynamic programming model that minimizes the cost of providing waste treatment to meet specified dissolved oxygen concentration standards in a stream is developed. The model is solved for a simplified example based on data from the Willamette River. Implications of the model on policy formulation are discussed. (Key words: Computers, digital; economics; oxygen; quality of water)
Mathematical models are developed to predict the probability distribution of minimum dissolved oxygen concentrations occurring downstream from any particular wastewater treatment facility. Each of the models is based on different assumptions of average daily stream and sewage flow conditions. Using a hypothetical example, distributions of minimum dissolved oxygen concentrations in a stream are determined for 1, 2, and 3 consecutive‐day periods. Knowledge of the cost required to reduce the probability of having less than some desired level of stream quality for various consecutive‐day periods can be used as a basis for selecting the degree of wastewater treatment as well as for establishing more realistic stream quality standards. (Key words: Quality of streams; probabilistic models)
Two linear programming models are presented for determining the amount of wastewater treatment required to achieve at minimum cost any particular set of stream dissolved oxygen standards within a river basin. Derived from the generalized Streeter-Phelps differential equations used to describe the rates of dissolved oxygen depletion and recovery of streams, these models are adaptable to any river basin configuration. They can be used not only in determining system costs for various quality standards but also for measuring the cost sensitivity to changes in the design stream and wastewater flows and treatment facility location. An example illustrates the use of these models.
The problems of management of tuberculosis in developing nations are studied utilizing the tools of systems analysis. The tuberculosis system consists of interacting components which are the "states of nature" of the disease. The interaction of these components determine the future state of the disease. Controls in the form of therapy, vaccinations or prophylaxis may be superimposed on the natural processes, thus altering the future course of the disease. A descriptive mathematical model describing the flows between the various categories is used to predict the trends both with and without intervention. An optimization model is derived from the descriptive model under the assumption that a program of reduction of active cases has been specified. The optimization model selects the forms of control which achieve the specified reduction program at least cost. Optimization is accomplished via linear programming. The model is general in that the parameters, costs and initial conditions may be varied for different situations. The descriptive mathematical model and the optimization model which determines the most efficient controls are intended to improve decision-making in public health management of tuberculosis.
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