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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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). https://doi.org/10.1007/BF02190100