Simulation- Based Inexact Two- Stage Chance- Constraint Quadratic Programming for Sustainable Water Quality Management under Dual Uncertainties

Water quality planning is complicated itself but further challenged by the existence of uncertainties and nonlinearities in terms of model formulation and solution. In this study, a simulation-based inexact two-stage chance-constraint quadratic programming (SITCQP) approach was developed for water quality management. The SITCQP model was a hybrid of two-stage stochastic programming (TSP), chance-constraint programming (CCP), inexact quadratic programming (IQP), and multisegment stream water quality simulation. A water quality simulation model was provided for reflecting the relationship between the pollution-control actions before wastewater discharge and the environmental responses after the discharge. Interval quadratic polynomials were employed to reflect the uncertainties and nonlinearities associated with the costs for wastewater treatment. Uncertainties derived from water quality standards were characterized as random variables with normal distributions. The proposed approach was applied to a hypothetical case in water quality management. The modeling solutions were presented as combinations of deterministic, interval and distributional information, which could facilitate predictions for different forms of uncertainties. The results were valuable for helping decision makers generate alternatives between wastewater treatment and stream water quality management.