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Estimation of Multiresponse Simulation Metamodels Using Control Variates

Author

Listed:
  • Acácio M. De O. Porta Nova

    (Departmento de Matemática, Instituto Superior Técnico, 1096 Lisboa CODEX, Portugal)

  • James R. Wilson

    (School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907)

Abstract

This paper provides a unified development of the method of control variates for simulation experiments in which the objective is estimation of a multiresponse metamodel---that is, a linear model for an output vector of simulation performance measures expressed in terms of an input vector of decision variables for the target system. In contrast to previous treatments of this topic, we allow both the input and output of the metamodel to be multidimensional so that control variates can be applied to multipopulation, multiresponse simulation experiments. Assuming that the responses and controls are jointly normal with a homogeneous covariance structure across the points of the experimental design, we develop control variates procedures for point and confidence-region estimation and for hypothesis testing on the coefficients of a postulated metamodel. We derive a generalized minimum variance ratio to quantify the maximum efficiency that is achievable with a given set of controls, and we formulate a generalized loss factor to measure the degradation in efficiency that occurs when the optimal control coefficients are estimated by the method of least squares. A detailed example illustrates the application of these results.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:11:p:1316-1333
    DOI: 10.1287/mnsc.35.11.1316
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    Citations

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    Cited by:

    1. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    2. 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)," Other publications TiSEM 3e563d88-0029-47f6-a66b-e, Tilburg University, School of Economics and Management.
    3. Reis dos Santos, M. Isabel & Porta Nova, Acacio M.O., 2006. "Statistical fitting and validation of non-linear simulation metamodels: A case study," European Journal of Operational Research, Elsevier, vol. 171(1), pages 53-63, May.
    4. Bettonvil, Bert & del Castillo, Enrique & Kleijnen, Jack P.C., 2009. "Statistical testing of optimality conditions in multiresponse simulation-based optimization," European Journal of Operational Research, Elsevier, vol. 199(2), pages 448-458, December.
    5. Tew, Jeffrey D., 1995. "Simulation metamodel estimation using a combined correlation-based variance reduction technique for first and higher-order metamodels," European Journal of Operational Research, Elsevier, vol. 87(2), pages 349-367, December.
    6. Athanassios N. Avramidis & Kenneth W. Bauer & James R. Wilson, 1991. "Simulation of stochastic activity networks using path control variates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 183-201, April.
    7. Badiru, Adedeji B. & Sieger, David B., 1998. "Neural network as a simulation metamodel in economic analysis of risky projects," European Journal of Operational Research, Elsevier, vol. 105(1), pages 130-142, February.

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