Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty
研究了将条件风险价值作为风险度量的多阶段随机线性规划，提出了五种嵌套L型分解算法，并应用于美国亚利桑那州图森市东南部的水资源分配问题，以控制严重缺水事件的风险。
We study a risk-averse approach to multistage stochastic linear programming, where the conditional value-at-risk is incorporated into the objective function as the risk measure. We consider five decompositions of the resulting risk-averse model to solve it via the nested L-shaped method. We introduce separate approximations of the mean and the risk measure and also investigate the effectiveness of multiple cuts. As an application, we formulate a water allocation problem by risk-averse multistage programming, which has the advantage of controlling high-risk severe water shortage events. We apply the proposed formulation to the southeastern portion of Tucson, AZ to best use the limited water resources available to that region. In numerical experiments we (1) present a comparative computational study of the risk-averse nested L-shaped variants and (2) analyze the risk-averse approach to the water allocation problem.