Water quality is a major issue due to the pollution of water caused by increasing human activities. Rivers are considered one of the major sources of the water necessary for different fields. The main objective of the optimum design for water quality in a river is to minimize the total costs of treating pollutants in the water such that the permissible water quality levels are maintained at all points in the river, and the water supply quantity and quality requirements are satisfied.
To obtain an optimum design for water quality in rivers, a model is established that represents a river basin subject to pollution. There are many techniques for optimization. In this paper, both the dynamic programming and the linear programming are employed mainly for this purpose. The dynamic programming is used by two different methods. The first method is the ordinary technique that called recursive dynamic programming, while the second method is a combination between the dynamic programming and the linear programming. Also, the linear programming is applied to the model, where an optimum solution is obtained. The optimum solutions are obtained by the PC for the model applying the three developed techniques. These optimum solutions are compared showing high degree of tendency.
It is concluded that combination between the dynamic programming and the linear programming is an effective tool to get the optimum design for water quality in rivers. It is easy, simple, accurate, fast and is solved by a common PC software. It is recommended to provide more study for the combination between the dynamic programming and the linear programming. Also, it is recommended to investigate its application to problems with maximization objective functions.
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