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Stochastic Kriging for Simulation Metamodeling

Author

Listed:
  • Bruce Ankenman

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Barry L. Nelson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Jeremy Staum

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We extend the basic theory of kriging, as applied to the design and analysis of deterministic computer experiments, to the stochastic simulation setting. Our goal is to provide flexible, interpolation-based metamodels of simulation output performance measures as functions of the controllable design or decision variables, or uncontrollable environmental variables. To accomplish this, we characterize both the intrinsic uncertainty inherent in a stochastic simulation and the extrinsic uncertainty about the unknown response surface. We use tractable examples to demonstrate why it is critical to characterize both types of uncertainty, derive general results for experiment design and analysis, and present a numerical example that illustrates the stochastic kriging method.

Suggested Citation

  • Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:2:p:371-382
    DOI: 10.1287/opre.1090.0754
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    References listed on IDEAS

    as
    1. W C M van Beers & J P C Kleijnen, 2003. "Kriging for interpolation in random simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 255-262, March.
    2. Jeffrey D. Tew & James R. Wilson, 1992. "Validation of Simulation Analysis Methods for the Schruben-Margolin Correlation-Induction Strategy," Operations Research, INFORMS, vol. 40(1), pages 87-103, February.
    3. Justin Boesel & Barry L. Nelson & Seong-Hee Kim, 2003. "Using Ranking and Selection to “Clean Up” after Simulation Optimization," Operations Research, INFORMS, vol. 51(5), pages 814-825, October.
    4. Ardavan Nozari & Steven F. Arnold & C. Dennis Pegden, 1987. "Statistical Analysis for Use with the Schruben and Margolin Correlation Induction Strategy," Operations Research, INFORMS, vol. 35(1), pages 127-139, February.
    5. van Beers, Wim C.M. & Kleijnen, Jack P.C., 2008. "Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1099-1113, May.
    6. Ward Whitt, 1989. "Planning Queueing Simulations," Management Science, INFORMS, vol. 35(11), pages 1341-1366, November.
    7. Kleijnen, Jack P. C. & van Beers, Wim C. M., 2005. "Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments," European Journal of Operational Research, Elsevier, vol. 165(3), pages 826-834, September.
    Full references (including those not matched with items on IDEAS)

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