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

Author

Listed:
  • Zhichao Zheng

    (Lee Kong Chian School of Business, Singapore Management University, Singapore 178899)

  • Karthik Natarajan

    (Engineering Systems and Design, Singapore University of Technology and Design, Singapore 487372)

  • Chung-Piaw Teo

    (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 119245)

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 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.

Suggested Citation

  • Zhichao Zheng & Karthik Natarajan & Chung-Piaw Teo, 2016. "Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty," Operations Research, INFORMS, vol. 64(6), pages 1406-1421, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1406-1421
    DOI: 10.1287/opre.2016.1528
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    References listed on IDEAS

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    Cited by:

    1. Lili Zhang & Zhengrui Chen & Dan Shi & Yanan Zhao, 2023. "An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    2. Sheng Liu & Long He & Zuo-Jun Max Shen, 2021. "On-Time Last-Mile Delivery: Order Assignment with Travel-Time Predictors," Management Science, INFORMS, vol. 67(7), pages 4095-4119, July.
    3. Yuanguang Zhong & Zhichao Zheng & Mabel C. Chou & Chung-Piaw Teo, 2018. "Resource Pooling and Allocation Policies to Deliver Differentiated Service," Management Science, INFORMS, vol. 64(4), pages 1555-1573, April.

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