A Mixed-Integer Conic Programming Formulation for Computing the Flexibility Index under Multivariate Gaussian Uncertainty

TL;DR

This paper introduces a mixed-integer conic programming approach to compute the flexibility index under multivariate Gaussian uncertainty, directly capturing correlations and providing bounds for stochastic flexibility.

Contribution

The methodology directly characterizes ellipsoidal uncertainty sets using MICP, improving over approximation methods and enabling bounds on stochastic flexibility indices.

Findings

Efficient computation of the flexibility index for Gaussian uncertainties.

Provides a lower bound for the stochastic flexibility index.

Method can be generalized to other uncertainty sets.

Abstract

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.