Stochastic models and numerical solutions for production planning with applications to the paper industry

Computers and Chemical Engineering

Volumn 27, Issue 11, 2003, Pages 1693-1706

  Yin, K Karen ^a   Liu, Hu ^a   Yin, G George ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b WAYNE STATE UNIVERSITY   (United States)

Author keywords

HJB equation; Markov chain; Numerical method; Optimal policy; Paper manufacturing; Production planning

Indexed keywords

ALGORITHMS; PLANNING; STOCHASTIC CONTROL SYSTEMS; SYSTEMS ANALYSIS;

RANDOM DEMAND;

PRODUCTION ENGINEERING;

CONTROL SYSTEM; MATHEMATICAL ANALYSIS; MODELING; PAPER MANUFACTURE; PULP AND PAPER INDUSTRY; STOCHASTIC METHOD;

ALGORITHM; ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; PAPER INDUSTRY; PLANNING; PROBABILITY; REACTOR; STOCHASTIC MODEL;

EID: 0142043493     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(03)00136-4     Document Type: Article

References (26)

1. Akella, R., & Kumar, P. R. (1986). Optimal control of production rate in a failure-prone manufacturing system. IEEE Transactions on Automatic Control AC-31, 116-126.
2. Applequist, G., Samikoglu, O., Pekny, J., & Reklaitis, G. (1997). Issues in the use, design and evolution of process scheduling and planning systems. ISA Transactions 36 (2), 81-121.
3. Balasubramanian, J., & Grossmann, I. E. (2002). Scheduling to minimize expected completion time in flowshop plants with uncertain processing times. Computers and Chemical Engineering 26, 41-57.
4. Bassett, M. H., Pekny, J. F., & Reklaitis, G. V. (1997). Using detailed scheduling to obtain realistic operating policies for a batch processing facility. Industrial Engineering and Chemical Research 36 (5), 1717-1726.
5. Bertsekas, D. (1976). Dynamic programming and stochastic control. New York, NY: Academic Press.
6. Bertsekas, D. (1987). Dynamic programming: deterministic and stochastic models. Prentice-Hall.
7. Bielecki, T. R., & Kumar, P. R. (1988). Optimality of zero-inventory policies for unreliable manufacturing systems. Operations Research 36, 532-541.
8. Boukas, E. K., Yang, H., & Zhang, Q. (1995). Minimax production planning in failure prone manufacturing systems. Journal of Optimal Theory Applied 87, 269-286.
9. Davis, M. H. A. (1993). Markov models and optimization. New York, NY: Chapman & Hall.
10. Fleming, W. H., & Rishel, R. W. (1975). Deterministic and stochastic optimal control. New York: Springer.
11. Gershwin, S. B. (1994). Manufacturing systems engineering. Englewood Cliffs: Prentice-Hall.
12. Gupta, A., Maranas, C. D., & McDonald, C. M. (2000). Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management. Computers and Chemical Engineering 24 (12), 2613-2621.
13. Ho, Y. C., & Cao, X. R. (1991). Perturbation analysis of discrete event dynamic systems. Boston, MA: Kluwer.
14. Kushner, H. J. (1990). Numerical methods for stochastic control problems in continuous time. SIAM Journal of Control Optimization 28, 999-1048.
15. Kushner, H. J., & Dupuis, P. G. (1992). Numerical methods for stochastic control problems in continuous time. New York: Springer.
16. Kushner, H. J., & Yin, G. (1997). Stochastic approximation algorithms and applications. New York: Springer.
17. Leiviskä, K. (1999). Process control. Helsinki, Finland: Fapet Oy.
18. Petkov, S. B., & Mararas, C. D. (1997). Multiperiod planning and scheduling of multiproduct batch plants under demand uncertainty. Industrial and Engineering Chemistry Research 36 (11), 4864-4881.
19. Sethi, S. P., & Zhang, Q. (1994). Hierarchical decision making in stochastic manufacturing systems. Boston: Birkhäuser.
20. Yan, H. M., Yin, G., & Lou, S. X. C. (1994). Using stochastic optimization to determine threshold values for control of unreliable manufacturing systems. Journal of Optimal Theory Applied 83, 511-539.
21. Yang, H., Yin, G., Yin, K., & Zhang, Q. (2003). Control of singularly perturbed Markov chains: a numerical study. The ANZIAM Journal 45, 49-74 (formerly Journal of Australian Mathematics Society Series B: Applied Mathematics).
22. Yin, K., Yin, G., & Zhang, Q. (1995). Approximating the optimal threshold levels under robustness cost criteria for stochastic manufacturing systems. Proceedings of the IFAC Conference of Youth Automation YAC '95, 450-454.
23. Yin, G., & Zhang, Q. (1997). Mathematics of stochastic manufacturing systems, Proceedings of the 1996 AMS-SIAM summer seminar in applied mathematics, lectures in applied mathematics. Providence, RI: American Mathematics Society.
24. Yin, G., & Zhang, Q. (1998). Continuous-time Markov chains and applications: a singular perturbation approach. New York: Springer.
25. Zhang, Q., & Yin, G. (1994). Turnpike sets in stochastic manufacturing systems with finite time horizon. Stochastics Stochastic Report 51, 11-40.
26. Zhang, Q., Yin, G., & Boukas, E. K. (2001). Optimal control of a marketing-production system. IEEE Transactions on Automatic Control 46, 416-427.