Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty

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.