A regularized decomposition method for minimizing a sum of polyhedral functions
Mathematical Programming: Series A and B
MSLiP: a computer code for the multistage stochastic linear programming problem
Mathematical Programming: Series A and B
Dual Stochastic Dominance and Related Mean-Risk Models
SIAM Journal on Optimization
Convexity and decomposition of mean-risk stochastic programs
Mathematical Programming: Series A and B
A two-stage stochastic programming model for transportation network protection
Computers and Operations Research
The integer L-shaped method for stochastic integer programs with complete recourse
Operations Research Letters
Mean-CVaR portfolio selection: A nonparametric estimation framework
Computers and Operations Research
Robust vertex p-center model for locating urgent relief distribution centers
Computers and Operations Research
Computers and Industrial Engineering
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Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse two-stage stochastic programming model, where we specify the conditional-value-at-risk (CVaR) as the risk measure. We construct two decomposition algorithms based on the generic Benders-decomposition approach to solve such problems. Both single-cut and multicut versions of the proposed decomposition algorithms are presented. We adapt the concepts of the value of perfect information (VPI) and the value of the stochastic solution (VSS) for the proposed risk-averse two-stage stochastic programming framework and define two stochastic measures on the VPI and VSS. We apply the proposed model to disaster management, which is one of the research fields that can significantly benefit from risk-averse two-stage stochastic programming models. In particular, we consider the problem of determining the response facility locations and the inventory levels of the relief supplies at each facility in the presence of uncertainty in demand and the damage level of the disaster network. We present numerical results to discuss how incorporating a risk measure affects the optimal solutions and demonstrate the computational effectiveness of the proposed methods.