Inexact joint-probabilistic stochastic programming for water resources management under uncertainty

In this study, an inexact two-stage integer program with joint-probabilistic constraint (ITIP-JPC) is developed for supporting water resources management under uncertainty. This method can tackle uncertainties expressed as joint probabilities and interval values, and can reflect the reliability of satisfying (or the risk of violating) system constraints under uncertain events and/or parameters. Moreover, it can be used for analysing various policy scenarios that are associated with different levels of economic consequences when the pre-regulated targets are violated. The developed ITIP-JPC is applied to a case study of water resources allocation within a multi-stream, multi-reservoir and multi-user context, where joint probabilities exist in both water availabilities and storage capacities. The results indicate that reasonable solutions have been generated for both binary and continuous variables. They can help generate desired policies for water allocation and flood diversion with a maximized economic benefit and a minimized system-disruption risk.