IFMP: Interval-fuzzy multistage programming for water resources management under uncertainty

An interval-fuzzy multistage programming (IFMP) method is developed for water resources management under uncertainty. This method improves upon the existing multistage stochastic programming methods by allowing uncertainties presented as discrete intervals, fuzzy sets, and probability distributions to be effectively incorporated within its optimization framework. The IFMP method can adequately reflect dynamic variations of system conditions, particularly for large-scale multistage problems with sequential structures. The uncertain information can be incorporated within a multi-layer scenario tree; revised decisions are permitted in each time period based on the realized values of the uncertain events. Moreover, this method can be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. A case study of water resources management is then provided for demonstrating applicability of the developed method. For all scenarios under consideration, corrective actions are allowed to be taken dynamically in reference to the pre-regulated policies and the realized uncertainties. The results can help quantify the relationships among system benefit, satisfaction degree, and constraint-violation risk. Thus, desired decision alternatives can be generated under different conditions of supply-demand dynamics.