Padé approximants for the transient optimization of hedging control policies in manufacturing

IEEE Transactions on Automatic Control

Volumn 42, Issue 4, 1997, Pages 440-457

  El Férik, Sami ^b   Malhamé, Roland P ^a,b,c  

^a IEEE

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^c GERAD   (Canada)

Author keywords

Finite horizon manufacturing flow control; Hedging control policies; Pad approximants

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; INVENTORY CONTROL; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; TIME VARYING CONTROL SYSTEMS;

FINITE HORIZON MANUFACTURING FLOW CONTROL; HEDGING CONTROL POLICIES; MACHINE MODE INVENTORY LEVELS; PADE APPROXIMANTS; SINGLE PART MULTIPLE FAILURE MODE MANUFACTURING SYSTEMS;

PRODUCTION CONTROL;

EID: 0031116903     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.566655     Document Type: Article

References (27)

1. C. T. Chen, Linear System Theory and Design. New York: Holt, Rinehart and Winston, 1984.
2. G. A. Baker, Jr., Essentials of Padé Approximants. New York: Academic, 1975.
3. R. G. Bartle, The Elements of Integration. New York: Wiley, 1966.
4. A. Priestely, Introduction to Complex Analysis. New York: Oxford Sci., 1990.
5. G. J. Olsder and R. Suri, "Time-optimal control of flexible manufacturing systems with failure prone machines," in Proc. 19th IEEE Conf. Decision Contr., Dec. 1980.
6. G. Liberopoulos and J. Hu, "On the ordering of optimal hedging points in a class of manufacturing flow control models," IEEE Trans. Automat. Contr., vol. 40, pp. 282-286, Feb. 1995.
7. J. B. Kimemia and S. B. Gershwin, "An algorithm for the computer control of production in flexible manufacturing systems," IIE Trans., vol. 15, no. 4, pp. 353-362, Dec. 1983.
8. J. Q. Hu, P. Vakili, and G. X. Yu, "Optimality of hedging policies in the production control of failure prone manufacturing systems," IEEE Trans. Automat. Contr., vol. 39, pp. 1875-1880, Sept. 1994.
9. J. R. Perkins and R. Srikant, "Scheduling multiple part-types in an unreliable single machine manufacturing system," IEEE Trans. Automat. Contr., 1995, submitted.
10. M. C. Caramanis and A. Sharifnia, "Near-optimal manufacturing flow controller design," Int. J. Flexible Manufacturing Syst., vol. 3, no. 4, pp. 321-336, 1991.
11. R. P. Malhamé, "Ergodicity of hedging point policies in single part multiple state manufacturing systems," IEEE Trans. Automat. Contr., vol. 38, pp. 340-343, Feb. 1993.
12. N. Srivatsan and Y. Dallery, "Partial characterization of optimal policies in unreliable multiple-part-type systems," Tech. Rep. Lab. Manufacturing Productivity LMP94-004, 1994.
13. P. Brémaud, R. P. Malhamé, and L. Massoulié, "A manufacturing system with general stationary failure process: Stability and IPA of hedging control policies," IEEE Trans. Automat. Contr., vol 42, pp. 155-170, Feb. 1997.
14. P. Glasserman, "Hedging-point production control with multiple failure modes," IEEE Trans. Automat. Contr., vol. 40, pp. 707-711, Apr. 1995.
15. Q. Zhang and G. Yin, "Turnpike sets in stochastic manufacturing systems with finite time horizon," Stochastics and Stochastics Rep., vol. 51, pp. 11-40, July 1994.
16. R. Akella and P. R. Kumar, "Optimal control of production rate in a failure prone manufacturing system," IEEE Trans. Automat. Contr., vol. AC-31, pp. 116-126, Feb. 1986.
17. R. P. Malhamé, "A jump-driven Markovian electric load model," Advances Appl. Probability, vol. 22, pp. 564-586, 1990.
18. R. P. Malhamé and E. K. Boukas, "A Markov renewal analysis of the production control of a flexible manufacturing system under hedging point policies," GERAD Rep., G89-37, Nov. 1981.
19. _, "A renewal theoretic analysis of a class of manufacturing systems," IEEE Trans. Automat. Contr., vol. 36, pp. 353-362, May 1991.
20. R. Rishel, "Dynamic programming and minimum principles for systems with jump Markov disturbances," SIAM J. Contr., vol. 13, pp. 338-371, Feb. 1975.
21. S. B. Gershwin, Manufacturing Systems Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1994.
22. S. P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems. Boston: Birkhauser, 1994.
23. A. Sharifnia, "Production control of manufacturing system with multiple machine states," IEEE Trans. Automat. Contr., vol. 33, pp. 620-625, July 1988.
24. T. Bielecki and P. R. Kumar, "Optimality of zero-inventory policies for unreliable manufacturing systems," Operat. Res., vol. 26, pp. 532-540, July-Aug. 1988.
25. W. B. Gong, S. Nonanukul, and A. Yan, "Padé approximation for stochastic discrete-event systems," IEEE Trans. Automat. Contr., vol. 40, no. 8, pp. 1349-1358, 1995.
26. W. H. Fleming, S. P. Sethi, and H. M. Soner, "An optimal stochastic production planning problem with randomly fluctuating demand, " SIAM J. Contr. Optimization, vol. 25, no. 6, pp. 1494-1502, Nov. 1987.
27. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing. Cambridge: Cambridge Univ. Press, 1988.