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

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 captur...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Pulsipher, Joshua L, Zavala, Victor M
Format: Article
Language:English
Subjects:
Computation
Flexibility
Lower bounds
Methodology
Mixed integer
Multivariate analysis
Random variables
Uncertainty
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.12702