Mo, S.; Duan, H.; Shen, B., and Wang, D., 2015. Interval two-stage stochastic integer programming for urban water resources management under uncertainty.

In this study, an interval-parameter two-stage stochastic integer programming model (ITSIP) was developed for urban water resource planning under uncertainty. ITSIP incorporates pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios. Each scenario has a different economic penalty when the agreed water-allocation targets are violated. Methods of interval-parameter and stochastic programming were applied to tackle uncertainties described by both interval value and probability distributions, while binary variables were used to model processes such as shunting. The developed method can provide a link between economic cost and the associated penalties attributed to the violation of pre-regulated policies. The model was used in a case study of an urban water supply system that withdraws water from multiple sources. A number of scenarios corresponding to different river inflow levers were examined, and the results indicated that different inflow levels could lead to differing water allocation schemes with varied system costs and failure risks. The model proved to be valuable for identifying management regimes that minimize cost under different decision scenarios with various levels of stream flow.