  In this study, we consider two classes of multicriteria two-stage stochastic
programs in finite probability spaces with multivariate risk constraints. The
first-stage problem features a multivariate stochastic benchmarking constraint
based on a vector-valued random variable representing multiple and possibly
conflicting stochastic performance measures associated with the second-stage
decisions. In particular, the aim is to ensure that the associated random
outcome vector of interest is preferable to a specified benchmark with respect
to the multivariate polyhedral conditional value-at-risk (CVaR) or a
multivariate stochastic order relation. In this case, the classical
decomposition methods cannot be used directly due to the complicating
multivariate stochastic benchmarking constraints. We propose an exact unified
decomposition framework for solving these two classes of optimization problems
and show its finite convergence. We apply the proposed approach to a stochastic
network design problem in a pre-disaster humanitarian logistics context and
conduct a computational study concerning the threat of hurricanes in the
Southeastern part of the United States. Our numerical results on these
large-scale problems show that our proposed algorithm is computationally
scalable.
