Abstract
We deduce control equations governed by ordinary differential equations that determine the moments of the inventory levels in a flow control model of a flexible manufacturing system. Then we discuss how to use these control equations to study the expected inventory level set and the optimal inventory level control problem with quadratic cost functions.
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References
R. J. Aumann, Integrals of Set-Valued Function, J. Math. Anal. Appl. Vol. 12, pp. 1–12, 1965.
R. Bellman, Introduction to the Mathematical Theory of Control Processes, Vol. II. Nonlinear Processes, Academic Press, New York, 1971.
E. K. Boukas and Q. J. Zhu, Production set of failure prone flexible manufacturing systems, Research report, GERAD, Montreal, 1993.
M. H. A. Davis, Markov Models and Optimization, Chapman and Hall, New York, 1993.
J. L. Doob, Stochastic Process, John Wiley & Sons, Inc., New York, 1953.
S. B. Gershwin, Manufacturing Systems Engineering, Prentice Hall, 1993.
W. A. Gruver and E. Sachs, Algorithmic methods in optimal control, Research notes in math. Vol. 47, Pitman, Boston, 1980.
D. Q. Mayne and R. W. Brockett, Geometric Methods in System Theory, Proceedings of the NATO Advanced Study Institute, London, 1973, D. Reidel Publishing, Boston, 1973.
R. T. Rockafellar, Convex Analysis, Princeton Mathematics Ser. Vol. 28, Princeton University Press, 1970.
S.P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhauser, Boston, 1994.
Q. J. Zhu, N. Zhang and Y. He, Algorithm for Determining the Reachability Set of a Linear Control System, Journal of Optimization Theory and Applications, Vol. 72, pp. 333–353, 1992.
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© 1996 Springer-Verlag London Limited
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Zhu, Q.J. (1996). Studying flexible manufacturing systems via deterministic control problems. 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/BFb0015118
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DOI: https://doi.org/10.1007/BFb0015118
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