Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty
针对随机目标系数服从多元正态分布的线性优化问题，提出用最小二乘正态逼近和二次估计器来近似最优值分布，并通过计算持久性值实现，数值实验表明在项目完成时间分布估计上优于现有方法。
This paper is motivated by the following question: How to construct good approximation for the distribution of the solution value to linear optimization problem when the random objective coefficients follow a multivariate normal distribution? Using Stein’s Identity, we show that the least squares normal approximation of the random optimal value can be computed by estimating the persistency values of the corresponding optimization problem. We further extend our method to construct a least squares quadratic estimator to improve the accuracy of the approximation; in particular, to capture the skewness of the objective. Computational studies show that the new approach provides more accurate estimates of the distributions of project completion times compared to existing methods.