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.
Distribution Approximation, Persistency, Stein's Identity, Project Management, Statistical Timing Analysis
Business | Operations and Supply Chain Management
ZHENG, Zhichao; Natarajan, Karthik; and TEO, Chung-Piaw.
Least squares approximation to the distribution of project completion times with Gaussian uncertainty. (2016). Operations Research. 64, (6), 1406-1421. Research Collection Lee Kong Chian School Of Business.
Available at: http://ink.library.smu.edu.sg/lkcsb_research/5126
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