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Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping

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  • van Beers, Wim C.M.
  • Kleijnen, Jack P.C.

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, 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.
  • Handle: RePEc:eee:ejores:v:186:y:2008:i:3:p:1099-1113
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    References listed on IDEAS

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    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. 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.
    3. 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.
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    Citations

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    Cited by:

    1. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Discussion Paper 2008-95, Tilburg University, Center for Economic Research.
    2. 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.
    3. Kleijnen, J.P.C., 2009. "Sensitivity Analysis of Simulation Models," Discussion Paper 2009-11, Tilburg University, Center for Economic Research.
    4. 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.
    5. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    6. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. repec:eee:ejores:v:262:y:2017:i:2:p:575-585 is not listed on IDEAS

    More about this item

    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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