A numerical method in optimal production and setup scheduling of stochastic manufacturing systems

IEEE Transactions on Automatic Control

Volumn 42, Issue 10, 1997, Pages 1452-1455

  Yan, H ^a   Zhang, Q ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

HJB equation; Machine setup; Numerical method; Production planning; Scheduling

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; RANDOM PROCESSES; SCHEDULING;

HAMILTON JACOBI BELLMAN (HJB) EQUATION; MACHINE SETUP; STOCHASTIC MANUFACTURING SYSTEMS;

PRODUCTION CONTROL;

EID: 0031259285     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.633837     Document Type: Article

References (20)

1. 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, 1986.
2. S. X. Bai and M. Elhafsi, "Real-time scheduling of a manufacturing system with nonresumable setup changes," Res. Rep. (93-28), Univ. Florida, 1993.
3. E. K. Boukas and A. Haurie, "Manufacturing flow control and preventive maintenance: A stochastic control approach," IEEE Trans. Automat. Contr., vol. 35, pp. 1024-1031, 1990.
4. S. Connolly, Y. Dallery, and S. B. Gershwin, "A real-time policy for performing setup changes in a manufacturing system," in Proc. 31st IEEE Conf. Decision Contr., 1992.
5. M. H. A. Davis, Markov Models and Optimization. New York: Chapman & Hall, 1993.
6. D. Gatarek, "Optimality conditions for impulsive control of piecewise-deterministic processes," Math. Contr. Signals Syst., vol. 5, pp. 217-232, 1992.
7. S. B. Gershwin, Manufacturing Systems Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1994.
8. A. Haurie and C. van Delft, "Turnpike properties for a class of piecewise deterministic control systems arising in manufacturing flow control," Ann. Oper. Res., vol. 29, pp. 351-373, 1991.
9. J. Hu and M. Caramanis, "Dynamic set-up scheduling of flexible manufacturing systems: Design and stability of near optimal general round robin policies," Discrete Event Systems, IMA Vols. in Math. and its Applications Series, P. R. Kumar and P. Varaiya, Eds. New York: Springer-Verlag, 1995.
10. J. G. Kimemia and S. B. Gershwin, "An algorithm for the computer control production in flexible manufacturing systems," IIE Trans., vol. 15, pp. 353-362, 1983.
11. H. J. Kushner and P. G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time. New York: Springer-Verlag, 1992.
12. S. M. Lenhart, "Viscosity solutions associated with switching control problems for piecewise-deterministic processes," Houston J. Math., vol. 13, pp. 405-426, 1987.
13. G. Liberopoulos, "Flow control of failure prone manufacturing systems: Controller design theory and applications," Ph.D. dissertation, Boston Univ., 1993.
14. J. L. Menaldi, "Some estimates for finite difference approximations," SIAM J. Contr. Optim., vol. 27, pp. 579-607, 1989.
15. S. P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems. Boston: Birkhauser, 1994.
16. A. Sharifnia, "Production control of a manufacturing system with multiple machine states," IEEE Trans. Automat. Contr., vol. 33, pp. 620-625, 1988.
17. A. Sharifnia, M. Caramanis, and S. B. Gershwin, "Dynamic setup scheduling and flow control in manufacturing systems," J. Discrete Event Dynamic Syst., vol. 1, pp. 149-175, 1991.
18. N. Srivatsan and Y. Dallery, "Partial characterizations of optimal control policies in unreliable multiple part type systems," Tech. Rep. LMP-94-004, MIT, 1994.
19. N. Srivatsan and S. B. Gershwin, "Selection of setup times in a hierarchically controlled manufacturing system," in Proc. 29th IEEE Conf. Decision Contr., 1990.
20. H. Yan and Q. Zhang, "Production and setup scheduling in manufacturing systems: A numerical method," Tech. Rep., Univ. Georgia.