  We present a methodology for computing the flexibility index when uncertainty
is characterized using multivariate Gaussian random variables. Our approach
computes the flexibility index by solving a mixed-integer conic program (MICP).
This methodology directly characterizes ellipsoidal sets to capture
correlations in contrast to previous methodologies that employ approximations.
We also show that, under a Gaussian representation, the flexibility index can
be used to obtain a lower bound for the so-called stochastic flexibility index
(i.e., the probability of having feasible operation). Our results also show
that the methodology can be generalized to capture different types of
uncertainty sets.
