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Customized Sequential Designs for Random Simulation Experiments : Kriging Metamodelling and Bootstrapping

Author

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  • van Beers, W.C.M.

    (Tilburg University, Center For Economic Research)

  • Kleijnen, J.P.C.

    (Tilburg University, Center For Economic Research)

Abstract

This paper proposes a novel method to select an experimental design for interpolation in random simulation, especially discrete event simulation.(Though the paper focuses on Kriging, this design approach may also apply to other types of metamodels such as linear regression models.)Assuming that simulation requires much computer time, it is important to select a design with a small number of observations (or simulation runs).The proposed method is therefore sequential.Its novelty is that it accounts for the specific input/output behavior (or response function) of the particular simulation at hand; i.e., the method is customized or application-driven.A tool for this customization is bootstrapping, which enables the estimation of the variances of predictions for inputs not yet simulated.The new method is tested through two classic simulation models: example 1 estimates the expected steady-state waiting time of the M/M/1 queueing model; example 2 estimates the mean costs of a terminating (s, S) inventory simulation.For these simulations the novel design indeed gives better results than Latin Hypercube Sampling (LHS) with a prefixed sample of the same size.
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Suggested Citation

  • van Beers, W.C.M. & Kleijnen, J.P.C., 2004. "Customized Sequential Designs for Random Simulation Experiments : Kriging Metamodelling and Bootstrapping," Discussion Paper 2004-63, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:372530d0-3a48-43c5-a91a-456d48489b8e
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    References listed on IDEAS

    as
    1. Kleijnen, Jack P.C. & Deflandre, David, 2006. "Validation of regression metamodels in simulation: Bootstrap approach," European Journal of Operational Research, Elsevier, vol. 170(1), pages 120-131, April.
    2. D den Hertog & J P C Kleijnen & A Y D Siem, 2006. "The correct Kriging variance estimated by bootstrapping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 400-409, April.
    3. 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.
    4. Jack P. C. Kleijnen & Susan M. Sanchez & Thomas W. Lucas & Thomas M. Cioppa, 2005. "State-of-the-Art Review: A User’s Guide to the Brave New World of Designing Simulation Experiments," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 263-289, August.
    5. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    6. van Beers, W.C.M., 2005. "Kriging metamodeling for simulation," Other publications TiSEM bba6cefc-7b24-4ec1-836d-5, Tilburg University, School of Economics and Management.
    7. Sungmin Park & John W. Fowler & Gerald T. Mackulak & J. Bert Keats & W. Matthew Carlyle, 2002. "D-Optimal Sequential Experiments for Generating a Simulation-Based Cycle Time-Throughput Curve," Operations Research, INFORMS, vol. 50(6), pages 981-990, December.
    8. Ferri, M. & Piccioni, M., 1992. "Optimal selection of statistical units : An approach via simulated annealing," Computational Statistics & Data Analysis, Elsevier, vol. 13(1), pages 47-61, January.
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    Cited by:

    1. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    2. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Other publications TiSEM e49ba0fc-853c-4a13-b564-d, Tilburg University, School of Economics and Management.
    3. Arreola-Risa, Antonio & Giménez-García, Víctor M. & Martínez-Parra, José Luis, 2011. "Optimizing stochastic production-inventory systems: A heuristic based on simulation and regression analysis," European Journal of Operational Research, Elsevier, vol. 213(1), pages 107-118, August.
    4. Kleijnen, J.P.C., 2009. "Sensitivity Analysis of Simulation Models," Other publications TiSEM 2016cf94-0329-4aa0-a4ea-4, Tilburg University, School of Economics and Management.
    5. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    6. Song, Kunling & Zhang, Yugang & Shen, Linjie & Zhao, Qingyan & Song, Bifeng, 2021. "A failure boundary exploration and exploitation framework combining adaptive Kriging model and sample space partitioning strategy for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    7. Hernandez, Andres F. & Grover, Martha A., 2013. "Error estimation properties of Gaussian process models in stochastic simulations," European Journal of Operational Research, Elsevier, vol. 228(1), pages 131-140.
    8. Scott L. Rosen & Christopher P. Saunders & Samar K Guharay, 2015. "A Structured Approach for Rapidly Mapping Multilevel System Measures via Simulation Metamodeling," Systems Engineering, John Wiley & Sons, vol. 18(1), pages 87-101, January.
    9. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    10. Vieira Jr., Hélcio & Sanchez, Susan & Kienitz, Karl Heinz & Belderrain, Mischel Carmen Neyra, 2011. "Generating and improving orthogonal designs by using mixed integer programming," European Journal of Operational Research, Elsevier, vol. 215(3), pages 629-638, December.
    11. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
    12. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    13. Liao, Hao & Wu, Xingtong & Wang, Bing-Hong & Wu, Xiangyang & Zhou, Mingyang, 2019. "Solving the speed and accuracy of box-covering problem in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 954-963.
    14. Jing Xie & Peter I. Frazier & Stephen E. Chick, 2016. "Bayesian Optimization via Simulation with Pairwise Sampling and Correlated Prior Beliefs," Operations Research, INFORMS, vol. 64(2), pages 542-559, April.
    15. Jason R. W. Merrick, 2009. "Bayesian Simulation and Decision Analysis: An Expository Survey," Decision Analysis, INFORMS, vol. 6(4), pages 222-238, December.
    16. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
    17. Chen, Xi & Zhou, Qiang, 2017. "Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 262(2), pages 575-585.

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    More about this item

    Keywords

    simulation; statistical methods; bootstrap;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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