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In this study, we consider two classes of multicriteria two-stage stochasticprograms in finite probability spaces with multivariate risk constraints. Thefirst-stage problem features a multivariate stochastic benchmarking constraintbased on a vector-valued random variable representing multiple and possiblyconflicting stochastic performance measures associated with the second-stagedecisions. In particular, the aim is to ensure that the associated randomoutcome vector of interest is preferable to a specified benchmark with respectto the multivariate polyhedral conditional value-at-risk (CVaR) or amultivariate stochastic order relation. In this case, the classicaldecomposition methods cannot be used directly due to the complicatingmultivariate stochastic benchmarking constraints. We propose an exact unifieddecomposition framework for solving these two classes of optimization problemsand show its finite convergence. We apply the proposed approach to a stochasticnetwork design problem in a pre-disaster humanitarian logistics context andconduct a computational study concerning the threat of hurricanes in theSoutheastern part of the United States. Our numerical results on theselarge-scale problems show that our proposed algorithm is computationallyscalable.

Two-stage Stochastic Programming under Multivariate Risk Constraints with an Application to Humanitarian Relief Network Design