A two-stage inexact-probabilistic programming (TIPP) method was developed for water quality management in Zhangweinan River Basin, through coupling two-stage stochastic programming with inexact chance-constrained programming. The developed TIPP can handle uncertainties presented as both discrete intervals and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system's constraints for accomplishing a maximized system benefit. It can also be used for analyzing policy scenarios that are associated with different levels of economic penalties when the promised targets are violated. Interval solutions under different constraint-violation levels have been obtained. They can be used for generating decision alternatives and thus help managers to identify desired policies under various environmental, economic, and system-reliability constraints.
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