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Periodic maintenance and repair rate control in stochastic manufacturing systems


In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.

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  1. Hu, J. Q., Vakili, P., andYu, G. X.,Optimality of Hedging Point Policies in the Production Control of Failure-Prone Manufacturing Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 1875–1880, 1994.

    Google Scholar 

  2. Hu, J. Q., andXiang, D.,Monotonicity of Optimal Flow Control for Failure-Prone Production Systems, Journal of Optimization Theory and Applications, Vol. 86, pp. 57–71, 1995.

    Google Scholar 

  3. Sethi, S. P., andZhang, Q.,Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhäuser, Boston, Massachusetts, 1994.

    Google Scholar 

  4. Boukas, E. K.,Techniques for Flow Control and Preventive Maintenance in Manufacturing Systems, Control and Dynamic Systems, Vol. 48, pp. 327–366, 1991.

    Google Scholar 

  5. Boukas, E. K.,Control of Systems with Controlled Jump Markov Disturbances, International Journal of Control Theory and Advanced Technology, Vol. 9, pp. 577–595, 1993.

    Google Scholar 

  6. Boukas, E. K.,A Stochastic Modeling for Flexible Manufacturing Systems, Working paper, 1993.

  7. Boukas, E. K., andHaurie, A.,Manufacturing Flow Control and Preventive Maintenance: A Stochastic Control Approach, IEEE Transactions on Automatic Control, Vol. 35, pp. 1024–1031, 1990.

    Google Scholar 

  8. Boukas, E. K., Zhu, Q., andZhang, Q.,A Piecewise Deterministic Markov Process Model for Flexible Manufacturing Systems with Preventive Maintenance, Journal of Optimization Theory and Application, Vol. 81, pp. 259–275, 1994.

    Google Scholar 

  9. Davis, M. H. A.,Markov Models and Optimization, Chapman and Hall, New York, New York, 1993.

    Google Scholar 

  10. Fleming, W. H., andSoner, H. M.,Controlled Markov Processes and Viscosity Solutions, Springer Verlag, New York, New York, 1992.

    Google Scholar 

  11. Boukas, E. K., Zhang, Q., andYin, G.,On Robust Control Problems in Stochastic Manufacturing Systems, Recent Advances in Control and Optimization of Manufacturing Systems, Lecture Notes in Control and Information Sciences, Vol. 214, 1996.

  12. Kushner, H. J., andDupuis, P. G.,Numerical Methods for Stochastic Control Problems in Continuous Time, Springer Verlag, New York, New York, 1992.

    Google Scholar 

  13. Akella, R., andKumar, P. R.,Optimal Control of Production Rate in a Failure-Prone Manufacturing System, IEEE Transactions on Automatic Control, Vol. 31, pp. 106–126, 1986.

    Google Scholar 

  14. Gershwin, S. B.,Manufacturing Systems Engineering, Prentice Hall, Englewood Cliffs, New Jersey, 1994.

    Google Scholar 

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Communicated by C. T. Leondes

Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.

Research of this author was supported in part by the University of Georgia.

Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.

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Boukas, E.K., Yang, J., Zhang, Q. et al. Periodic maintenance and repair rate control in stochastic manufacturing systems. J Optim Theory Appl 91, 347–361 (1996).

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