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A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations

Author

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  • S. S. Lavenberg

    (IBM Thomas J. Watson Research Center)

  • P. D. Welch

    (IBM Thomas J. Watson Research Center)

Abstract

This is a survey paper on the application of control variables to increase the efficiency of discrete event simulations. The emphasis is on the practical problems and potential of applying the method in the simulation of complex systems. The basic theory of control variables is reviewed and the equivalence of control variables and multiple estimators is discussed. Techniques for generating control variables are described. Inefficiencies resulting from the statistical estimation of control variable coefficients and the problem of confidence interval generation are treated. This is done both within the context of the method of independent replications and the regenerative method. The application literature is reviewed and the conditions under which control variables could be profitably applied in practical simulations are described. Finally, there is a set of recommended directions for future research.

Suggested Citation

  • S. S. Lavenberg & P. D. Welch, 1981. "A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations," Management Science, INFORMS, vol. 27(3), pages 322-335, March.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:3:p:322-335
    DOI: 10.1287/mnsc.27.3.322
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    Cited by:

    1. Erik Hintz & Marius Hofert & Christiane Lemieux & Yoshihiro Taniguchi, 2022. "Single-Index Importance Sampling with Stratification," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3049-3073, December.
    2. Tsai, Shing Chih & Chu, I-Hao, 2012. "Controlled multistage selection procedures for comparison with a standard," European Journal of Operational Research, Elsevier, vol. 223(3), pages 709-721.
    3. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    4. Pellizzari, P., 2005. "Static hedging of multivariate derivatives by simulation," European Journal of Operational Research, Elsevier, vol. 166(2), pages 507-519, October.
    5. Assereto, Martina & Byrne, Julie, 2021. "No real option for solar in Ireland: A real option valuation of utility scale solar investment in Ireland," Renewable and Sustainable Energy Reviews, Elsevier, vol. 143(C).
    6. Kämpke, Thomas, 1989. "Multiple use of random numbers in discrete-event simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(3), pages 171-176.
    7. Grant, Floyd H. & Solberg, James J., 1983. "Variance reduction techniques in stochastic shortest route analysis: application procedures and results," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(4), pages 366-375.
    8. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    9. Shing Chih Tsai & Chen Hao Kuo, 2012. "Screening and selection procedures with control variates and correlation induction techniques," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 340-361, August.
    10. Zhang, M.M. & Wang, Qunwei & Zhou, Dequn & Ding, H., 2019. "Evaluating uncertain investment decisions in low-carbon transition toward renewable energy," Applied Energy, Elsevier, vol. 240(C), pages 1049-1060.
    11. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    12. Russell Davidson & James G. Mackinnon, 1990. "Regression-Based Methods for Using Control and Antithetic Variates in Monte Carlo Experiments," Working Paper 781, Economics Department, Queen's University.
    13. Amano, Tomoyuki & Taniguchi, Masanobu, 2011. "Control variate method for stationary processes," Journal of Econometrics, Elsevier, vol. 165(1), pages 20-29.
    14. Tsai, Shing Chih, 2011. "Selecting the best simulated system with weighted control-variate estimators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 705-717.
    15. Carla Curado & Mírian Oliveira & Dara G. Schniederjans & Eduardo Kunzel Teixeira, 2024. "Control variable use and reporting in operations management: a systematic literature review and revisit," Management Review Quarterly, Springer, vol. 74(3), pages 1809-1839, September.
    16. Zhang, M.M. & Zhou, P. & Zhou, D.Q., 2016. "A real options model for renewable energy investment with application to solar photovoltaic power generation in China," Energy Economics, Elsevier, vol. 59(C), pages 213-226.
    17. Mingming Zhang & Dequn Zhou & Hao Ding & Jingliang Jin, 2016. "Biomass Power Generation Investment in China: A Real Options Evaluation," Sustainability, MDPI, vol. 8(6), pages 1-22, June.
    18. Zhang, M.M. & Zhou, D.Q. & Zhou, P. & Chen, H.T., 2017. "Optimal design of subsidy to stimulate renewable energy investments: The case of China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 71(C), pages 873-883.
    19. Michael P. Bailey & Marcelo C. Bartroli & Keebom Kang & Alexander J. Callahan, 1992. "Establishing Reliability Goals for Naval Major‐Caliber Ammunition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 877-892, December.
    20. Ben-Alexander Cassell & Michael P. Wellman, 2012. "Asset pricing under ambiguous information: an empirical game-theoretic analysis," Computational and Mathematical Organization Theory, Springer, vol. 18(4), pages 445-462, December.

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