Inexact quadratic joint-probabilistic programming for water quality management under uncertainty in the Xiangxi River, China

An inexact quadratic joint-probabilistic programming model for water quality management (IQJWQ) is developed and applied to supporting multiple-point-source waste reduction in the Xiangxi River, China. The IQJWQ is a hybrid of interval quadratic programming, joint probabilistic programming and multi-segment water quality simulation. It has advantages in reflecting uncertainties expressed as joint probabilities of system risk, probability distributions of water quality standards, interval parameters and nonlinearities in the objective function. An interactive and derivative algorithm is employed for solving the IQJWQ model. The results indicate that the Pingyikou chemical plant and Liucaopo chemical plant contribute more to pollution of the main stream in the Xiangxi River, which should be the prior plants to reduce the wastewater discharge and enhance the wastewater treatment efficiencies. Meanwhile, the environmental agencies should choose the joint probability carefully to balance the tradeoff between production development and pollution control. Compared with the conventional chance-constrained programming method, the IQJWQ exhibits an increased robustness in handling the overall system risk in the optimization process. Although this study is the first application of the IQJWQ to water quality management, the proposed methods in the IQJWQ can also be applicable to many other environmental management problems under uncertainty.