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Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models

Author

Listed:
  • Christian van Delft

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • A. Haurie
  • Pierre L'Ecuyer

    (DIRO - Département d'Informatique et de Recherche Opérationnelle [Montreal] - UdeM - Université de Montréal)

Abstract

This paper deals with a class of piecewise determinstic control systems for which the optimal control can be approximated through the use of an optimization-by-simulation approach. The feedback control law is restricted to belong to an a priori fixed class of feedback control laws depending on a (small) finite set of parameters. Under some general conditions developed in this paper, infinitesimal perturbation analysis (IPA) can be used to estimate the gradient of the objective function with respect to these parameters for finite horizon simulation and the consistency of the IPA estimators, as the simulation length goes to infinity, is assured. Also, the parameters can be optimized through a stochastic approximation (SA) algorithm combined with IPA. We prove that in this context, under appropriate conditions, such an approach converges towards the optimum.

Suggested Citation

  • Christian van Delft & A. Haurie & Pierre L'Ecuyer, 1994. "Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models," Post-Print hal-00471357, HAL.
    • Handle: RePEc:hal:journl:hal-00471357
    DOI: 10.1007/BF01516011
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    Citations

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    Cited by:

    1. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Other publications TiSEM 015cb8ee-38d7-41b1-b9fc-7, Tilburg University, School of Economics and Management.
    2. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    3. Mourani, Iyad & Hennequin, Sophie & Xie, Xiaolan, 2008. "Simulation-based optimization of a single-stage failure-prone manufacturing system with transportation delay," International Journal of Production Economics, Elsevier, vol. 112(1), pages 26-36, March.
    4. Cao, Xi-Ren, 1996. "Perturbation analysis of discrete event systems: Concepts, algorithms, and applications," European Journal of Operational Research, Elsevier, vol. 91(1), pages 1-13, May.
    5. Haurie, A., 1995. "Time scale decomposition in production planning for unreliable flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 82(2), pages 339-358, April.

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