Abstract
Flow control of flexible manufacturing systems (FMSs) addresses an important real-time scheduling requirement of modern manufacturing facilities, which are prone to failures and other controllable or stochastic discrete events affecting production capacity, such as change of setup and maintenance scheduling. Flow controllers are useful both in the coordination of interconnected flexible manufacturing cells through distributed scheduling policies and in the hierarchical decomposition of the planning and scheduling problem of complex manufacturing systems. Optimal flow-control policies are hedging-point policies characterized by a generally intractable system of stochastic partial differential equations. This article proposes a near optimal controller whose design is computationally feasible for realistic-size systems. The design exploits a decomposition of the multiple-part-type problem to many analytically tractable one-part-type problems. The decomposition is achieved by replacing the polyhedra production capacity sets with inscribed hypercubes. Stationary marginal densities of state variables are computed iteratively for successive trial controller designs until the best inscribed hypercubes and the associated optimal hedging points are determined. Computational results are presented for an illustrative example of a failureprone FMS.
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References
Akella, R. and Kumar, P., “Optimal Control of Production Rate in a Failure Prone Manufacturing System,” IEEE Transactions on Automatic Control, Vol. 31, No. 2, pp. 116–126 (February 1986).
Algoet, P., “Flow Balance Equations for the Steady-State Distribution of a Flexible Manufacturing System,” IEEE Transactions on Automatic Control, Vol. 34, No. 8, pp. 917–921 (July 1989).
Bielecki, T. and Kumar, P., “Optimality of Zero Inventory Policies for Unreliable Manufacturing Systems,” Operations Research, Vol. 36, pp. 532–541 (July–August 1988).
Caramanis, M. and Liberopoulos, G., “Perturbation Analysis for the Design of Flexible Manufacturing System Flow Controllers,” forthcoming in Operations Research 1991.
Caramanis, M. and Sharifnia, A., “Analytic Derivation of Near Optimal Production Flow Control Policies for Flexible Manufacturing Systems,” Proceedings of the Winter ASME Meetings, Boston, MA, PED, Vol. 25, pp. 451–460 (December 13–18, 1987).
Caramanis, M. and Sharifnia, A., “Design of Near Optimal Flow Controllers for Flexible Manufacturing Systems,” Proceedings of the ORSA/TIMS Special Interest Conference on FMS, Cambridge, MA, K. Stecke and R. Suri (Eds.), Elsevier Science Publishers B.V., Amsterdam, pp. 321–326 (August 1989).
Gershwin, S., Akella, R., and Choong, Y., “Short Term Production Scheduling of an Automated Manufacturing Facility,” IBM Journal of Research and Development, Vol. 29, No. 4, pp. 392–400 (July 1985).
Gershwin, S.B., “Hierarchical Flow Control: A Framework for Scheduling and Planning Discrete Events in Manufacturing Systems,” Proceedings of the IEEE, Vol. 77, No. 1, pp. 195–209, (January 1989).
Hall, R.W., Zero Inventories, Dow-Jones Irwin, Homewood, IL (1983).
Kimemia, J. and Gershwin, S., “An Algorithm for the Computer Control of Production in Flexible Manufacturing Systems,” IIE Transactions, Vol. 15, No. 4, pp. 353–362 (December 1983).
Liberopoulos, G., “Efficient Design of Near-Optimal Manufacturing Flow Controllers Using Benders' Decomposition and Decision Space Reduction Techniques,” Boston University, Department of Manufacturing Engineering, Working Paper BU-LMSP-WP-11–89, Boston, MA (September 1989).
Olsder, G.J. and Suri, R., “Time-Optimal Control of Parts Routing in a Manufacturing System with Failure-Prone Machines,” Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, NM (December 1980).
Rishel, R., “Dynamic Programming and Minimum Principles for Systems with Jump Markov Disturbances,” SIAM Journal of Control, Vol. 13, No. 2, pp. 338–371 (February 1975).
Sharifnia, A., “Production Control of a Manufacturing System with Multiple Machine States,” IEEE Transactions on Automatic Control, Vol. 33, No. 7, pp. 620–625 (July 1988).
Tsitsiklis, J., “Convexity of Characterization of Optimal Policies in a Dynamic Routing Problem,” Journal of Optimization Theory and Applications, Vol. 44, No. 1, pp. 105–135 (September 1984).
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Caramanis, M., Sharifnia, A. Near optimal manufacturing flow controller design. Int J Flex Manuf Syst 3, 321–336 (1991). https://doi.org/10.1007/BF00170212
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DOI: https://doi.org/10.1007/BF00170212