Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty

• 成果类型: Article
• 署名作者: Zheng, Zhichao; Natarajan, Karthik; Teo, Chung-Piaw
• 署名单位: Singapore Management University; Singapore University of Technology & Design; National University of Singapore
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2016.1528
• 发表日期: 2016
• 页码: 1406-1421
• 关键词: statistical timing analysis; optimization; ORDER

摘要

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.