In area of water resources management, decision-makers usually need to make plans under various uncertainties in order to achieve the maximal total net benefits and prevent possible losses under risks arising from the indeterminacy. In this paper, we have incorporated the conditional value-at-risk, which has been widely used in portfolio selection problems for effective risk management, in the interval two-stage stochastic programming framework to perform trade-offs between economic objectives and associated risks. Moreover, based on the late progresses in Grey linear system, we have developed a new method to obtain a solution of the proposed model. In particular, this new approach can provide a number of decision alternatives under different coefficients, which help decision-makers make proper water supply plans according to their personal preferences. Finally, numerical experiments have been presented to demonstrate the validity and applicability of the proposed model for maintaining balance between profits and risks, as well as the efficiency of the new method for dealing with such model.

在水资源管理领域，决策者通常需要在各种不确定性下制定计划，以实现最大的总净收益并防止不确定性带来的风险带来的可能损失。在本文中，我们在两个阶段的随机规划框架中纳入了条件风险价值，该条件风险价值已广泛用于有效风险管理的投资组合选择问题中，以在经济目标与相关风险之间进行权衡。此外，根据格雷线性系统的最新进展，我们开发了一种新方法来获得所提出模型的解。特别是，这种新方法可以在不同系数下提供许多决策选择，这有助于决策者根据个人喜好制定适当的供水计划。最后，通过数值实验证明了所提模型在维持利润与风险之间的平衡方面的有效性和适用性，以及处理该模型的新方法的有效性。