Entropy Based Optimization Model of Waste-Load Allocation

Environmental pollution can be perceived as the by-product of discharging and dumping material, heat and waste into the environment through human activities of production and consumption. When a compound is added to fresh water, it will be dissolved and diffused throughout the water body. The dissolution and diffusion imply an increase in the entropy of the matter (by virtue of its definition and the second law of thermodynamics) and an increase in the degree of pollution. This implies that water pollution results in an increase in entropy. Water is extensively used in cooling, washing, disposal of waste material and dissipation of waste heat. Water pollution can then be viewed as a source of increasing the entropy of the river. Thus, entropy can serve as a unified index for assessment of water pollution and a means of controlling it. It has also been used in information management and reducing the data redundancy with applications in water quality management. This paper explores the potential of measuring entropy for solving waste-load allocation problems. The objective function of the optimization model is to minimize the entropy of polluting the river. The model is used as an optimization tool to find the optimal removal fraction at the point sources in order to minimize the total increase in entropy of the river. The model is applied to a case study in southwestern Iran.