An inexact joint-probabilistic programming method for risk assessment in water resources allocation

In this study, an inexact joint probabilistic programming (IJPP) approach is developed for risk assessment and uncertainty reflection in water resources management systems. IJPP can dominate random parameters in the model's left- and right-hand sides of constraints and interval parameters in the objective function. It can also help examine the risk of violating joint probabilistic constraints, which allows an increased robustness in controlling system risk in the optimization process. Moreover, it can facilitate analyses of various policy scenarios that are associated with different levels of economic consequences when the promised targets are violated within a multistage context. The IJPP method is then applied to a case study of planning water resources allocation within a multi-reservoir and multi-period context. Solutions of system benefit, economic penalty, water shortage, and water-allocation pattern vary with different risks of violating water-demand targets from multiple competitive users. Results also demonstrate that different users possess different water-guarantee ratios and different water-allocation priorities. The results can be used for helping water resources managers to identify desired system designs against water shortage and for risk control, and to determine which of these designs can most efficiently accomplish optimizing the system objective under uncertainty.