Fuzzy-stochastic-based violation analysis method for planning water resources management systems with uncertain information

In this study, a fuzzy-stochastic-based violation analysis (FSVA) approach is developed for the planning of water resources management systems with uncertain information, based on a multistage fuzzy-stochastic integer programming (FSIP) model. In FSVA, a number of violation variables for the objective and constraints are allowed, such that in-depth analyses of tradeoffs among economic objective, satisfaction degree, and constraint-violation risk can be facilitated. Besides, the developed method can deal with uncertainties expressed as probability distributions and fuzzy sets; it can also reflect the dynamics in terms of decisions for water-allocation and surplus-flow diversion, through transactions at discrete points of a complete scenario set over a multistage context. The developed FSVA method is applied to a case study of water resources management within a multi-stream, multi-reservoir and multi-period context. The results indicate that the satisfaction degrees and system benefits would be different under varied violation levels; moreover, different violation levels can also lead to changed water-allocation and surplus-flow diversion plans. Violation analyses are also conducted to demonstrate that violating different constraints have different effects on system benefit and satisfaction degree.