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Robust Optimization in Simulation : Taguchi and Krige Combined

Author

Listed:
  • Dellino, G.
  • Kleijnen, Jack P.C.

    (Tilburg University, Center For Economic Research)

  • Meloni, C.

Abstract

Optimization of simulated systems is the goal of many methods, but most methods assume known environments. We, however, develop a “robust” methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world but replaces his statistical techniques by design and analysis of simulation experiments based on Kriging (Gaussian process model); moreover, we use bootstrapping to quantify the variability in the estimated Kriging metamodels. In addition, we combine Kriging with nonlinear programming, and we estimate the Pareto frontier. We illustrate the resulting methodology through economic order quantity (EOQ) inventory models. Our results suggest that robust optimization requires order quantities that differ from the classic EOQ. We also compare our results with results we previously obtained using response surface methodology instead of Kriging.
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Suggested Citation

  • Dellino, G. & Kleijnen, Jack P.C. & Meloni, C., 2009. "Robust Optimization in Simulation : Taguchi and Krige Combined," Discussion Paper 2009-82, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:d919b893-db2b-4d97-a392-4a55e2ad2494
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    References listed on IDEAS

    as
    1. Kleijnen, J.P.C. & Pierreval, H. & Zhang, J., 2009. "Methodology for Determining the Acceptability of Given Designs in Uncertain Environments," Other publications TiSEM e4f96b06-a05f-4da2-b651-8, Tilburg University, School of Economics and Management.
    2. 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.
    3. 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.
    4. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    5. 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, September.
    6. Garcia-Gonzalez, Javier & Parrilla, Ernesto & Mateo, Alicia, 2007. "Risk-averse profit-based optimal scheduling of a hydro-chain in the day-ahead electricity market," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1354-1369, September.
    7. Yin, Yafeng & Madanat, Samer M. & Lu, Xiao-Yun, 2009. "Robust improvement schemes for road networks under demand uncertainty," European Journal of Operational Research, Elsevier, vol. 198(2), pages 470-479, October.
    8. Kleijnen, J.P.C., 2009. "Sensitivity Analysis of Simulation Models," Discussion Paper 2009-11, Tilburg University, Center for Economic Research.
    9. Stinstra, Erwin & den Hertog, Dick, 2008. "Robust optimization using computer experiments," European Journal of Operational Research, Elsevier, vol. 191(3), pages 816-837, December.
    10. Yu, Gang, 1997. "Robust economic order quantity models," European Journal of Operational Research, Elsevier, vol. 100(3), pages 482-493, August.
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    Cited by:

    1. Janis Janusevskis & Rodolphe Le Riche, 2013. "Simultaneous kriging-based estimation and optimization of mean response," Journal of Global Optimization, Springer, vol. 55(2), pages 313-336, February.

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    More about this item

    Keywords

    Statistics; Design of experiments; Inventory-Production; Simulation; Decision analysis;
    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

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