A Two-Stage Stochastic Water Resources Planning Approach with Fuzzy Boundary Interval Based on Risk Control and Balanced Development

Establishing rational water resource allocation planning is critical for controlling risks within the water resource system and mitigating supply–demand pressures. Various risk elements within a water resource system transform, making it challenging to accurately represent the system response to different risk control measures using mathematical models. Therefore, in response to the risks and uncertainties present in the allocation process, this study aims to maximize comprehensive regional economic benefits. It combines risk control measures with balanced development strategies as model constraints and introduces approaches such as discrete intervals and fuzzy numbers to characterize multiple layers of uncertainty. Applying this model to a case study in Beijing, the results reveal that the overall water supply situation for the city in 2030 is not optimistic, particularly when both Beijing and the Danjiangkou Reservoir experience reduced inflows, potentially leading to a water supply deficit of [5.79 × 10 8 , 10.90 × 10 8 ] m 3 .