Mathematical Modeling for Water Quality Management under Interval and Fuzzy Uncertainties

In this study, an interval fuzzy credibility-constrained programming (IFCP) method is developed for river water quality management. IFCP is derived from incorporating techniques of fuzzy credibility-constrained programming (FCP) and interval-parameter programming (IPP) within a general optimization framework. IFCP is capable of tackling uncertainties presented as interval numbers and possibility distributions as well as analyzing the reliability of satisfying (or the risk of violating) system’s constraints. A real-world case for water quality management planning of the Xiangxi River in the Three Gorges Reservoir Region (which faces severe water quality problems due to pollution from point and nonpoint sources) is then conducted for demonstrating the applicability of the developed method. The results demonstrate that high biological oxygen demand (BOD) discharge is observed at the Baishahe chemical plant and Gufu wastewater treatment plant. For nonpoint sources, crop farming generates large amounts of total phosphorus (TP) and total nitrogen (TN). The results are helpful for managers in not only making decisions of effluent discharges from point and nonpoint sources but also gaining insight into the tradeoff between system benefit and environmental requirement.