Abstract
This paper concerns itself with the development of robust production and maintenance planning in manufacturing systems. Taking robustness into consideration, a new model for failure prone flexible manufacturing system with machines subject to breakdown and repair is proposed and analyzed. The machine capacity is assumed to be a Markov chain with finite state space, whereas the demand rate is treated as a bounded disturbance that can be deterministic or stochastic as long as it is adapted with respect to the Markov chain representing the machine capacity. The control variables are the rate of maintenance and the rate of production, and the cost function has a minimax structure. Under suitable conditions, it is shown that the value function is locally Lipschitz and satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. A sufficient condition for optimal control is obtained. Finally, an algorithm is given for solving the optimal control problem numerically.
Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada under grants OGP0036444 and FCAR NC0271 F.
Research of this author was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant A4169 and in part by the Office of Naval Research under Grant N00014-96-1-0263.
Research of this author was supported in part by the National Science Foundation under grant DMS-9224372, and in part by Wayne State University.
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© 1996 Springer-Verlag London Limited
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Boukas, E.K., Zhang, Q., Yin, G. (1996). On robust design for a class of failure prone manufacturing systems. In: Yin, G., Zhang, Q. (eds) Recent Advances in Control and Optimization of Manufacturing Systems. Lecture Notes in Control and Information Sciences, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015119
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DOI: https://doi.org/10.1007/BFb0015119
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