IDEAS home Printed from
   My bibliography  Save this paper

Statistical Testing of Optimality Conditions in Multiresponse Simulation-based Optimization (Revision of 2005-81)


  • Bettonvil, B.W.M.

    (Tilburg University, Center For Economic Research)

  • Del Castillo, E.
  • Kleijnen, J.P.C.

    (Tilburg University, Center For Economic Research)


This paper studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for test- ing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The pa- per focuses on "expensive" simulations, which have small sample sizes. The paper applies the classic t test to check whether the specific input combination is feasi- ble, and whether any constraints are binding; it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.

Suggested Citation

  • Bettonvil, B.W.M. & Del Castillo, E. & Kleijnen, J.P.C., 2007. "Statistical Testing of Optimality Conditions in Multiresponse Simulation-based Optimization (Revision of 2005-81)," Discussion Paper 2007-45, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:3e563d88-0029-47f6-a66b-ed001f03a5fb

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Acácio M. De O. Porta Nova & James R. Wilson, 1989. "Estimation of Multiresponse Simulation Metamodels Using Control Variates," Management Science, INFORMS, vol. 35(11), pages 1316-1333, November.
    2. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    3. Martin, Michael A., 2007. "Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6321-6342, August.
    4. 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.
    5. 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.
    6. Kao, Chiang & Chen, Shih-Pin, 2006. "A stochastic quasi-Newton method for simulation response optimization," European Journal of Operational Research, Elsevier, vol. 173(1), pages 30-46, August.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Stopping rule; metaheuristics; response surface methodology; design of experiments;

    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
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiucen:3e563d88-0029-47f6-a66b-ed001f03a5fb. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.