A risk-based fuzzy boundary interval two-stage stochastic water resources management programming approach under uncertainty

Establishing an optimal water allocation scheme is a challenging yet crucial task for effective risk management of water resources. The dynamic and complex interaction among various risk-related components in a water resources management system cannot be easily modeled to characterize the system response under different risk control settings. In this study, a risk-based fuzzy boundary interval two-stage stochastic water resources management programming (RFITSWMP) model is developed for the optimization of water consumption. This model incorporates a series of risk control constraints, such as water availability, maximum allowable penalty, and allowable benefit violation constraints into a fuzzy boundary interval two-stage stochastic programming framework for water resources management. It can address the uncertainties presented as fuzzy boundary intervals and probability distributions. It can also tackle the recourse action to minimize penalties based on interactive influences of different risk control measures, further generating optimal water allocation alternatives and guiding water resources management. This developed model is applied to a case study of water consumption optimization in the middle reaches of the Heihe River Basin in China. Feasible water allocation schemes under given risk levels, as well as the associated economic benefit, actual benefit and penalty loss are generated. The results can help decision makers to gain an insight into the inherent conflicts and tradeoffs amid risk, benefit and water allocation. The performance of developed model is further demonstrated by comparing it with a fuzzy boundary interval two stage stochastic water resources management programming (FITSWMP) model. In addition, a multiple factorial analysis (MFA) approach is employed to analyze the impacts of interactive risk parameters on the optimal decisions. The result disclosed that (1) the higher individual risk-parameter levels correspond to higher water shortage, penalty loss and benefit value-at-risk but higher economic benefit. (2) The combination of risk parameters can achieve robust water allocation and economic benefit as the constraints concerned with risk parameters affect and limited by each other. (3) The condition that water violated probability (p) is 0.2, penalty violated risk level (β) is 1 and benefit violated risk level (γ) is 1 has the highest water allocation and biggest economic benefit.