A stochastic decision-making framework for optimal multi-objective reservoir operation accounting for the tracking of uncertainty propagation and evolution from multiple sources

The operation of reservoirs involves real-time forecasting, decision-making, and operational processes, all of which are heavily influenced by interconnected uncertainties. These uncertainties pose significant challenges in formulating optimal decisions and introduce risks throughout the “Forecast-Operation-Decision-Making” (FODM) chain. To address multi-objective decision-making under uncertain conditions, a comprehensive modeling framework is proposed. This framework captures the propagation and evolution of uncertainties in the FODM chain through three interconnected sub-modules. Firstly, recognizing the dynamic nature of hydrological forecasting errors, we employ a robust martingale model to stochastically simulate runoff, providing crucial input conditions for reservoir operation. Secondly, a multi-objective stochastic optimization model is developed to account for uncertainties in forecasting, deriving the Pareto frontier under stochastic environments. A novel quantification method is introduced to address the dual uncertainties in performance values (PVs) and criterion weights (CWs). Additionally, a risk-based group decision-making model (MC-EDAS) is proposed, integrating Monte Carlo simulation to evaluate the distance from the average solution and address dual uncertainties. Two risk indicators are introduced to assess decision reliability. The framework also incorporates a two-stage decision-making process, facilitating the integration of preference information through iterative interactions between the decision group and the model. Numerical experiments using predefined risk indicators are conducted to analyze uncertainty propagation within the FODM chain. A case study in the Dadu River Basin, China, yields several key findings: (1) Forecasting errors transform non-inferior solutions on the Pareto frontier from discrete points into random variables with specific distributions, introducing uncertainty into PVs. (2) In the deterministic EDAS model, the top three ranked alternatives differ by a minimal margin of 0.01, but in the MC-EDAS model, this difference increases to approximately 0.15, highlighting the superior discriminability and provision of probabilistic decision information by the MC-EDAS model. (3) During numerical experiments, perturbation forecast uncertainty levels range from 50 to 400, leading to significant increases in the standard deviations of two objective function values and decision reliability indicators. The proposed framework comprehensively addresses the multiple uncertainties inherent in the FODM chain of reservoirs. By integrating stochastic simulation of runoff, multi-objective stochastic optimization, risk-based group decision-making, decision reliability analysis, and risk evolution assessment, it provides a unified and robust approach. The introduced risk indicators quantitatively track the propagation characteristics of uncertainties, enhancing the capability of reservoir operation decisions to avoid risks.