A Bayesian-based Two-stage Inexact Optimization Method For Water Quality Management

In recent years, the problem of water quality degradation in association with immoderate discharge of point and nonpoint source pollutions extrudes increasingly, which has posed serious threat to economic development, human health, and ecological sustainability, especially in China. Effective planning for water quality management has been an imperative task for facilitating sustainable socio-economic development in watershed systems. However, in water quality management problems, various uncertainties exist in a number of system components (social, economic, environmental, technical and political) as well as their interrelationships; the uncertainties can be further amplified by interactions among various uncertain and dynamic impact factors, thus affecting the environmental objectives and economic benefits. Therefore, this study is to advance a Bayesian-based two-stage inexact optimization (BTIO) method to handle such uncertainties in water quality management system for supporting rational local decision-making. The BTIO method is developed by integrating the Bayesian analysis approach and interval two-stage stochastic programming (ITSP). BTIO method is capable of addressing uncertainties caused by insufficient inputs in water quality model as well as uncertainties expressed as probabilistic distributions and interval numbers. The developed BTIO method is applied to a real case of water quality management for Xiangxi River basin in the Three Gorges Reservoir region to seek optimal water quality management schemes under various uncertainties. Interval solutions for production patterns under a range of probabilistic water quality constraints have been generated. The results demonstrate compromises between the overall system benefits and the system-failure risk due to inherent uncertainties that exist in various system components; phosphorus mining companies and chemical industries are the oriented incomes; chemical plants or phosphorus mining companies are the major contributors to TP and cropped zones and Livestock breeding are the dominant contributor to COD. Moreover, information about pollutant emission is accomplished, which would help managers to adjust production patterns of regional industry and local policies considering interactions of water quality requirement, economic benefit, and industry structure.