Sensitivity and covariance in stochastic complementarity problems with an application to North American natural gas markets
Sensitivity and covariance in stochastic complementarity problems with an application to North American natural gas markets
复制标题
DOI：
10.1016/j.ejor.2017.11.003
复制
发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
S. Sankaranarayanan;F. Feijoo;Sauleh Siddiqui
中科院分区：
文献类型：
--
作者：
S. Sankaranarayanan;F. Feijoo;Sauleh Siddiqui
我们提供了一个有效的方法来近似决策变量和不确定参数之间的协方差的解决方案的一般类随机非线性互补问题。我们还开发了一个灵敏度度量，通过确定由于输入参数方差变化而导致的输出方差变化来量化不确定性传播。解变量的协方差矩阵量化了输出中的不确定性，并将相关变量和参数配对。灵敏度度量有助于识别导致输出最大波动的参数。本文开发的方法优化了梯度和矩阵乘法的使用，这使得它特别适用于大规模的问题。在开发了这种方法之后，我们扩展了北美天然气模型（NANGAM）的确定性版本，以纳入由于需求函数，供应函数，基础设施成本和投资成本参数的不确定性而产生的影响。然后，我们使用敏感性指标来确定对均衡影响最大的参数。
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.