A two-factor stochastic production model with two time scales

A two-factor production model where one factor is characterized by a continuous state variable and corresponds to the fast mode via a controlled diffusion process, whereas the second factor is characterized by a discrete variable and corresponds to the slow mode via a controlled jump process.

[1]  R. Rishel Control of systems with jump Markov disturbances , 1975 .

[2]  P. Kokotovic,et al.  A singular perturbation approach to modeling and control of Markov chains , 1981 .

[3]  G. Yin,et al.  Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach , 1997 .

[4]  H. Kushner Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

[5]  Mark H. Davis Markov Models and Optimization , 1995 .

[6]  M. Caramanis,et al.  Production control of manufacturing systems with production rate-dependent failure rates , 1994, IEEE Trans. Autom. Control..

[7]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[8]  R. Rishel Dynamic Programming and Minimum Principles for Systems with Jump Markov Disturbances , 1975 .

[9]  Joseph Githu Kimemia,et al.  Hierarchial control of production in flexible manufacturing systems , 1982 .

[10]  J. Filar,et al.  Algorithms for singularly perturbed limiting average Markov control problems , 1990, 29th IEEE Conference on Decision and Control.

[11]  Qing Zhang,et al.  Continuous-Time Markov Chains and Applications , 1998 .

[12]  Qing Zhang,et al.  Multilevel Hierarchical Decision Making in Stochastic Marketing-Production Systems , 1995 .

[13]  M. K. Ghosh,et al.  Ergodic Control of Switching Diffusions , 1997 .

[14]  Jerzy A. Filar,et al.  Competitive Markov Decision Processes - Theory, Algorithms, and Applications , 1997 .

[15]  W. Fleming,et al.  An Optimal Stochastic Production Planning Problem with Randomly Fluctuating Demand , 1987 .

[16]  H. Soner Singular perturbations in manufacturing , 1993 .

[17]  J. Filar,et al.  Perturbation and stability theory for Markov control problems , 1992 .

[18]  G. Dantzig,et al.  THE DECOMPOSITION ALGORITHM FOR LINEAR PROGRAMS , 1961 .

[19]  Juan Ye Optimal control of piecewise deterministic Markov processes. , 1990 .

[20]  François Delebecque,et al.  Optimal control of markov chains admitting strong and weak interactions , 1981, Autom..

[21]  El-Kébir Boukas,et al.  Manufacturing flow control and preventing maintenance: a stochastic control approach , 1988 .

[22]  Stanley B. Gershwin,et al.  An algorithm for the computer control of a flexible manufacturing system , 1983 .

[23]  R. Suri,et al.  Time-optimal control of parts-routing in a manufacturing system with failure-prone machines , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[24]  G. Dantzig,et al.  The decomposition algorithm for linear programming: notes on linear programming and extensions-part 57. , 1961 .

[25]  H. Kushner Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems , 1990 .

[26]  D. Verms Optimal control of piecewise deterministic markov process , 1985 .

[27]  Jerzy A. Filar,et al.  Singularly perturbed Markov control problem: Limiting average cost , 1991 .

[28]  J. Filar,et al.  Control of singularly perturbed hybrid stochastic systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[29]  J. Quadrat,et al.  Contribution of stochastic control singular perturbation averaging and team theories to an example of large-scale systems: Management of hydropower production , 1978 .

[30]  Stanley B. Gershwin,et al.  Manufacturing Systems Engineering , 1993 .

[31]  M. K. Ghosh,et al.  Optimal control of switching diffusions with application to flexible manufacturing systems , 1993 .

[32]  J. Filar,et al.  Optimal Ergodic Control of Singularly Perturbed Hybrid Stochastic Systems , 1997 .