Sensitivity and covariance in stochastic complementarity problems with an application to North American natural gas markets

Sriram Sankaranarayanan, FELIPE ANDRES FEIJOO PALACIOS, Sauleh Siddiqui

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We provide an efficient method to approximate the covariance between decision variables and uncertain parameters in solutions to a general class of stochastic nonlinear complementarity problems. We also develop a sensitivity metric to quantify uncertainty propagation by determining the change in the variance of the output due to a change in the variance of an input parameter. The covariance matrix of the solution variables quantifies the uncertainty in the output and pairs correlated variables and parameters. The sensitivity metric helps in identifying the parameters that cause maximum fluctuations in the output. The method developed in this paper optimizes the use of gradients and matrix multiplications which makes it particularly useful for large-scale problems. Having developed this method, we extend the deterministic version of the North American Natural Gas Model (NANGAM), to incorporate effects due to uncertainty in the parameters of the demand function, supply function, infrastructure costs, and investment costs. We then use the sensitivity metrics to identify the parameters that impact the equilibrium the most.

Original languageEnglish
Pages (from-to)25-36
Number of pages12
JournalEuropean Journal of Operational Research
Volume268
Issue number1
DOIs
StatePublished - 1 Jul 2018
Externally publishedYes

Keywords

  • Approximation methods
  • Complementarity problems
  • Large scale optimization
  • Stochastic programming

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