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Convex and monotonic bootstrapped kriging

Author

Listed:
  • Kleijnen, Jack P.C.

    (Tilburg University, School of Economics and Management)

  • Mehdad, E.

    (Tilburg University, School of Economics and Management)

  • van Beers, W.C.M.

    (Tilburg University, School of Economics and Management)

Abstract

Distribution-free bootstrapping of the replicated responses of a given discrete-event simulation model gives bootstrapped Kriging (Gaussian process) metamodels; we require these metamodels to be either convex or monotonic. To illustrate monotonic Kriging, we use an M/M/1 queueing simulation with as output either the mean or the 90% quantile of the transient-state waiting times, and as input the traffic rate. In this example, monotonic bootstrapped Kriging enables better sensitivity analysis than classic Kriging; i.e., bootstrapping gives lower MSE and confidence intervals with higher coverage and the same length. To illustrate convex Kriging, we start with simulation-optimization of an (s, S) inventory model, but we next switch to a Monte Carlo experiment with a second-order polynomial inspired by this inventory simulation. We could not find truly convex Kriging metamodels, either classic or bootstrapped; nevertheless, our bootstrapped “nearly convex” Kriging does give a confidence interval for the optimal input combination.
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Suggested Citation

  • Kleijnen, Jack P.C. & Mehdad, E. & van Beers, W.C.M., 2012. "Convex and monotonic bootstrapped kriging," Other publications TiSEM 972e079d-0209-45bf-b25e-a, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:972e079d-0209-45bf-b25e-ae65c56b853a
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    References listed on IDEAS

    as
    1. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    2. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, December.
    3. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    4. Izzet Sahin, 1982. "On the Objective Function Behavior in ( s , S ) Inventory Models," Operations Research, INFORMS, vol. 30(4), pages 709-724, August.
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    Cited by:

    1. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Other publications TiSEM 6ac4e049-ad86-447f-aeec-a, Tilburg University, School of Economics and Management.

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    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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