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

Operations Research, , Vol. 64, No. 6, pp. 1406-1421, 2016

42 Pages Posted: 25 May 2016 Last revised: 17 Nov 2016

Zhichao Zheng

Singapore Management University

Karthik Natarajan

Singapore University of Technology and Design (SUTD)

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences

Date Written: February 9, 2013

Abstract

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 solving the persistency problem, first introduced by Bertsimas et al. (2006). 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.

Keywords: Distribution Approximation, Persistency, Stein's Identity, Project Management, Statistical Timing Analysis

Suggested Citation

Zheng, Zhichao and Natarajan, Karthik and Teo, Chung-Piaw, Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty (February 9, 2013). Operations Research, , Vol. 64, No. 6, pp. 1406-1421, 2016. Available at SSRN: https://ssrn.com/abstract=2783632

Zhichao Zheng (Contact Author)

Singapore Management University ( email )

Lee Kong Chian School of Business
50 Stamford Road
Singapore 178899, 178899
Singapore
68085474 (Phone)

HOME PAGE: http://sites.google.com/site/zhengzhichao1985

Karthik Natarajan

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Chung-Piaw Teo

NUS Business School - Department of Decision Sciences ( email )

15 Kent Ridge Drive
Mochtar Riady Building, BIZ 1 8-69
119245
Singapore

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