Bibliography

1

M. Abbad, T. R. Bielecki, and J. A. Filar, ``Perturbation and Stability Theory for Markov Control Problems", IEEE Trans. Auto. Contr., Vol. 37, (1992), 1421-1425.

2

I. Adiri and A. Ben-Israel, ``An Extension and Solution of Arrow-Karlin Type Production Models by the Pontryagin Maximum Principle", Cahiers du Center d'Etudes de Recherche Opérationnelle, Vol. 8, (1966), 147-158.

3

R. Akella and P. R. Kumar, ``Optimal Control of Production Rate in a Failure-Prone Manufacturing System,'' IEEE Trans. Auto. Contr., Vol. AC-31, (1986), 116-126.

4

E. Altman and V. Gaitsgory, ``Control of a Hybrid Stochastic System", Systems Control Letters, Vol. 20, (1993), 307-314.

5

E. Altman and V. Gaitsgory, ``Asymptotic Optimization of a Nonlinear Hybrid System Governed by a Markov Decision Process", SIAM J. Contr. Optim., Vol. 35, (1997), 2070-2085.

6

E. A. Ari and S. Axsater, `` Disaggregation under uncertainty in hierarchical production planning," European Journal of Operational Research, Vol. 35, (1988), 182-186.

7

K. J. Arrow, S. Karlin, and H. Scarf, Studies in Mathematical Theory of Inventory and Production, Stanford University Press, Stanford, CA, 1958.

8

P. Auger, Dynamics and Thermodynamics in Hierarchically Organized Systems, Pergamon Press, Oxford, England, 1989.

9

S. Bai, Scheduling Manufacturing Systems with Work-in-Process Inventory Control, Ph.D. Thesis, MIT Operations Research Center, Cambridge MA, 1991.

10

S. Bai and S. B. Gershwin, ``Scheduling Manufacturing Systems with Work-in-Process Inventory,'' Proc. of the 29th IEEE Conference on Decision and Control, Honolulu, HI, (1990), 557-564.

11

E. N. Barron and R. Jensen, ``Total Risk Aversion, Stochastic Optimal Control, and Differential Games," Appl. Math. Optim., Vol. 19, (1989), 313-327.

12

G. K. Basak, A. Bisi and M. K. Ghosh, ``Controlled Random Degenerate Diffusions Under Long-Run Average Cost," Stochastic and Stochastic Reports, Vol. 61, (1997), 121-140.

13

S. Bensoussan, M. Crouhy, and J.-M., Proth, Mathematical Theory of Production Planning, North-Holland, New York, NY, 1983.

14

S. Bensoussan, S. P. Sethi, R. Vickson, and N. A. Derzko, ``Stochastic Production Planning with Production Constraints,'' SIAM J. Contr. Optim., Vol. 22, (1984), 920-935.

15

T. R. Bielecki and J. A. Filar, ``Singularly Perturbed Markov Control Problem: Limiting Average Cost,'' Annals of Operations Research, Vol. 28, (1991), 153-168.

16

T. R. Bielecki and P. R. Kumar, ``Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, Vol. 36, (1988), 532-546.

17

A. Bisi, E. Presman, S. P. Sethi, and H. Zhang, ``Optimality in Two-Machine Flowshop with Limited Buffer," to appear in Annals of Operations Research, 1999a.

18

A. Bisi, S. P. Sethi, and H. Zhang, ``Existence of an Optimal Control in a Two-Machine Flowshop with Limited Buffer," Working Paper, School of Management, The University of Texas at Dallas, 1999b.

19

G. Bitran, E. A. Hass, and K. Matsuo, ``Production Planning of Style Goods with High Set-up Costs and Forecast Revisions", Operations Research, Vol. 34, (1986), 226-236.

20

G. Bitran and A. Hax, ``On the Design of Hierarchical Production Planning Systems", Decision Sciences, Vol. 8, (1977), 28-54.

21

G. Bitran and D. Tirupati, ``Hierarchical Production Planning,'' Chapter 10 in Logistics of Production and Inventory, S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin (Eds.), Vol. 4 in the Series Handbooks in Operations Research and Management Science, North-Holland, Amsterdam, (1993), 523-568.

22

E. K. Boukas, ``Techniques for Flow Control and Preventive Maintenance in Manufacturing Systems", Control and Dynamic Systems, Vol. 48, (1991), 327-366.

23

E. K. Boukas and A. Haurie, ``Manufacturing Flow Control and Preventive Maintenance: A Stochastic Control Approach", IEEE Trans. on Automatic Control, Vol. 35, (1990), 1024-1031.

24

E. K. Boukas, Q. Zhang, and Q. Zhou, ``Optimal Production and Maintenance Planning of Flexible Manufacturing Systems", Proc. of the 32nd IEEE Conference on Decision and Control, San Antonio, TX, Dec. 1993, 15-17.

25

E. K. Boukas, Q. Zhu, and Q. Zhang, ``A Piecewise Deterministic Markov Process Model for Flexible Manufacturing Systems with Preventive Maintenance", J. Optimization Theory and Applications, Vol. 82, (1994), 269-286.

26

P. N. D. Bukh, ``A Bibliography of Hierarchical Production Planning Techniques, Methodology, and Applications (1974-1991)", Technical Report, Institute of Management, University of Aarhus, Aarhus, Demark, 1992.

27

M. Caramanis and G. Liberopoulos, ``Perturbation Analysis for the Design of Flexible Manufacturing System Flow Controllers,'' Operations Research. Vol. 40, (1992), 1107-1125.

28

M. Caramanis and A. Sharifnia, ``Optimal Manufacturing Flow Controller Design,'' Int. J. Flex. Manuf. Syst. Vol. 3, (1991), 321-336.

29

M. Caramanis, A. Sharifnia, J. Hu, and S. B. Gershwin, ``Development of a Science Base for Planning and Scheduling Manufacturing Systems,'' Proc. of the 1991 NSF Design and Manufacturing Systems Conference, The University of Texas at Austin, Austin, TX, Jan. 9-11, (1991), 27-40.

30

H. Chen and A. Mandelbaum, ``Hierarchical Modeling of Stochastic Networks, Part I: Fluid models, Part II: Strong Approximations," in Stochastic Modeling and Analysis of Manufacturing Systems, D. D. Yao(ed.), Springer Series in Operations Research, Springer-Verlag, New York, NY, 1994.

31

Committee on the Next Decade in Operations Research, ``Operations Research: the Next Decade,'' Operations Research, Vol. 36, (1988), 619-637.

32

S. Y. Connolly, Y. Dallery, and S. B. Gershwin, ``A Real-time Policy for Performing Setup Changes in a Manufacturing System,'' Proc. of the 31st IEEE-CDC, Tucson, AZ, Dec. 16-18, 1992.

33

B. Darakananda, Simulation of Manufacturing Process under a Hierarchical Control Algorithm, M.S. Thesis, MIT Department of EECS, Cambridge, MA, 1989.

34

M. H. A. Davis, Markov Models and Optimization, Chapman & Hall, New York, 1993.

35

F. Delebecque and J. Quadrat, ``Optimal Control for Markov Chains Admitting Strong And Weak Interactions,'' Automatica, Vol. 17, (1981), 281-296.

36

C. Derman, Finite State Markovian Decision Processes, Academic Press, New York, NY, 1970.

37

Evans L. C. and P. E. Souganidis, ``Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations," Indiana Univ. Math. Journal, Vol. 33, (1984), 773-797.

38

Y. Feng and H. Yan, Optimal production control in a discrete manufacturing system with unreliable machines and random demands, Working Paper, Department of Systems Engineering and Engineering Management, the Chinese University of Hong Kong, Hong Kong, 1999.

39

J. A. Filar, A. Haurie, F. Moresino, and J. P. Vial, ``Singularly Perturbed Hybrid Systems Approximated by Structured Linear Programs", Proceedings of International Workshop on Markov Processes and Controlled Markov Chains, August 22-28, 1999, Changsha, Hunan, China.

40

W. H. Fleming (Chair), ``Future Directions in Control Theory: A Mathematical Perspective,'' SIAM Reports on Issues in the Mathematical Sciences, Philadelphia, PA, 1988.

41

W. H. Fleming and W. M. McEneaney, ``Risk-Sensitive Control on an Infinite Horizon," SIAM J. Contr. Optim., Vol. 33 ,(1995), 1881-1921.

42

W. H. Fleming, S. P. Sethi, and H. M. Soner, ``An Optimal Stochastic Production Planning Problem with Random Fluctuating Demand," SIAM J. Contr. Optim., Vol. 25, (1987), 1494-1502.

43

W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1992.

44

W. H. Fleming and P. E. Souganidis, ``On the Existence of Value Functions of Two-Player, Zero-Sum Stochastic Different Games," Indiana Univ. Math. Journal, Vol. 38, (1989), 293-314.

45

W. H. Fleming and Q. Zhang, ``Risk-Sensitive Production Planning of a Stochastic Manufacturing System," SIAM J. Contr. Optim., Vol. 36, (1998), 1147-1170.

46

N. T. Fong and X. Y. Zhou, ``Hierarchical Production Policies in Stochastic Two-Machine Flowshop with Finite Buffers," Journal of Optimization Theory and Applications, Vol. 89, (1996), 681-712.

47

N. T. Fong and X. Y. Zhou, ``Hierarchical Production Policies in Stochastic Two-Machine Flowshop with Finite Buffers II: Feedback Controls," Working Paper, Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, 1997.

48

L. F. Gelders and L. Van Wassenhove, ``Production Planning: A Review", European Journal of Operational Research, Vol. 7, (1981), 101-110.

49

S. B. Gershwin, ``Stochastic Scheduling and Setups in a Flexible Manufacturing System,'' Proc. of Second ORSA/TIMS Conference on Flexible Manufacturing Systems, Ann Arbor, MI, Aug., (1986), 431-442.

50

S. B. Gershwin, ``Hierarchical Flow Control: a Framework for Scheduling and Planning Discrete Events in Manufacturing Systems,'' Proceedings of the IEEE, Special Issue on Dynamics of Discrete Event Systems, Vol. 77, (1989), 195-209.

51

S. B. Gershwin, Manufacturing Systems Engineering, Prentice-Hall, Englewood Cliffs, NJ, 1994.

52

S. B. Gershwin, R. Akella, and Y. Choong, ``Short Term Production Scheduling of an Automated Manufacturing Facility,'' IBM J. Res. Dev., Vol. 29, (1985), 392-400.

53

S. B. Gershwin, M. Caramanis, and P. Murray, ``Simulation Experience with a Hierarchical Scheduling Policy for a Simple Manufacturing System,'' Proceedings of the 27th IEEE Conference on Decision and Control, Austin, TX, Vol. 3, (1988), 1841-1849.

54

H. Gfrerer and G. Zäpfel, ``Hierarchical Model for Production Planning in the Case of Uncertain Demand", Working Paper, Johannes Kepler Universität Linz, Linz, Austria, 1994.

55

M. K. Ghosh, A. Arapostathis and S. I. Marcus, ``Optimal Control of Switching Diffusions with Applications to Flexible Manufacturing Systems," SIAM J. on Contr. Optim., Vol. 31, (1993), 1183-1204.

56

M. K. Ghosh, A. Arapostathis, and S. I. Marcus, `` Ergodic Control of Switching Diffusions," SIAM J. on Contr. Optim., Vol. 35, (1997), 1952-1988.

57

J. M. Harrison and M. I. Taksar, ``Instantaneous Control of Brownian Motion", Mathematics of Operations Research, Vol. 8, (1983), 439-453.

58

J. M. Harrison, T. M. Sellke, and A. J. Taylor, ``Impulse Control of Brownian Motion", Mathematics of Operations Research, Vol. 8, (1983), 454-466.

59

J. M. Harrison and L. M. Wein, ``Scheduling Networks of Queues: Heavy Traffic Analysis of a Simple Open Network," Queuing Systems: Theory and Applications, Vol. 5, (1989), 265-280.

60

J. M. Harrison and L. M. Wein, ``Scheduling Networks of Queues: Heavy Traffic Analysis of a Two-Station Closed Network," Operations Research, Vol. 38, (1990), 1052-1064.

61

R. F. Hartl and S. P. Sethi, ``Optimal Control Problems with Differential Inclusions: Sufficiency Conditions and an Application to a Production-Inventory Model", Optimal Control Applications & Methods, Vol. 5, (1984), 289-307.

62

P. Hartman, Ordinary Differential Equations. 2nd Edition, Birkhäuser-Verlag, Boston, MA, 1982.

63

A. Haurie and Ch. van Delft, ``Turnpike Properties for a Class of Piecewise Deterministic Control Systems Arising in Manufacturing Flow Control,'' Annals of Operations Research, Vol. 29, (1991), 351-373.

64

A. C. Hax and D. Candea, Production and Inventory Management, Prentice-Hall, Englewood Cliffs, NJ, 1984.

65

F. S. Hillier and G. L. Lieberman, Introduction to Operations Research, McGraw-Hill, New York, NY, 1989.

66

C. C. Holt, F. Modigliani, J. F. Muth, and H. A. Simon, Planning Production, Inventories, and Workforce, Prentice-Hall, Inc. Englewood Cliffs, NJ, 1960.

67

J. Hu and M. Caramanis, ``Near Optimal Setup Scheduling for Flexible Manufacturing Systems,'' Proc. of the Third RPI International Conference on Computer Integrated Manufacturing, Troy, NY, May 20-22, 1992.

68

J. Jiang and S. P. Sethi, ``A State Aggregation Approach to Manufacturing Systems Having Machines States with Weak and Strong Interactions,'' Operations Research, Vol. 39, (1991), 970-978.

69

S. M. Johnson, ``Sequential Production Planning over Time at Minimum Cost", Management Science, Vol. 3, (1957), 435-437.

70

R. Z. Khasminskii, G. Yin, and Q. Zhang, Constructing Asymptotic Series for Probability of Markov Chains with Weak and Strong Interactions, Quart. Appl. Math. Vol. 38, (1997), 177-200.

71

J. G. Kimemia and S. B. Gershwin, ``An Algorithm for the Computer Control Production in Flexible Manufacturing Systems,'' IIE Trans. Vol. 15, (1983), 353-362.

72

P. Koktovic, ``Application of Singular Perturbation Techniques to Control Problems,'' SIAM Review, Vol. 26, (1984), 501-550.

73

E. Krichagina, S. Lou, S. P. Sethi, and M. I. Taksar, ``Production Control in a Failure-Prone Manufacturing System: Diffusion Approximation and Asymptotic Optimality," The Annals of Applied Probability, Vol. 3, (1993), 421-453.

74

E. Krichagina, S. Lou, and M. I. Taksar, ``Double Band Polling for Stochastic Manufacturing Systems in Heavy Traffic," Mathematics of Operations Research, Vol. 19, (1994), 560-596.

75

S. Kumar and P. R. Kumar, Performance Bounds for Queuing Networks and Scheduling Policies, IEEE Trans. Automatic Control, Vol. 39, 1994, 1600-1611.

76

H. J. Kushner and K. M. Ramachandran, ``Optimal and Approximately Optimal Control Policies for Queues in Heavy Traffic", SIAM Journal on Control and Optimization, Vol. 27, (1989), 1293-1381.

77

J. B. Lasserre and C. Mercé, Robust hierarchical production planning under uncertainty, Annals of Operations Research, Vol. 26, 1990, 73-87.

78

J. Lehoczky, S. P. Sethi, H. M. Soner, and M. I. Taksar, ``An Asymptotic Analysis of Hierarchical Control of Manufacturing Systems Under Uncertainty,'' Mathematics Operations Research, Vol. 16, (1991), 596-608.

79

G. Liberopoulos and M. Caramanis, ``Production Control of Manufacturing Systems with Production Rate Dependent Failure Rates", IEEE Trans. Automatic Control, Vol. 38, (1993), 889-895.

80

G. Liberopoulos and M. Caramanis, ``Dynamics and Design of a Class of Parameterized Manufacturing Flow Controllers," IEEE Trans. Automatic Control, Vol. 40, (1995), 201-272.

81

G. Liberopoulos and J. Hu, ``On the Ordering of Optimal Hedging Points in a Class of Manufacturing Flow Control Models", IEEE Trans. Automatic Control, Vol. 40, (1995), 282-286.

82

C. M. Libosvar, ``Hierarchies in Production Management and Control: a Survey,'' Technical Report, LIDS-P-1734, Lab. for Infor. and Decision Systems, MIT, Cambridge, MA, (1988).

83

Z. Lieber, ``An Extension of Modigliani and Hohn's Planning Horizons results", Management Science, Vol. 20, (1973), 319-330.

84

S. Lou and P. Kager, ``A Robust Production Control Policy for VLSI Wafer Fabrication", IEEE Trans. on Semiconductor Manufacturing, Vol. 2, (1989), 159-164.

85

S. Lou, S. P. Sethi, and Q. Zhang, ``Optimal Feedback Production Planning in a Stochastic Two Machine Flowshop,'' European Journal of Operational Research-Special Issue on Stochastic Control Theory and Operational Research, Vol. 73, (1994), 331-345.

86

S. Lou and G. van Ryzin, ``Optimal Control Rules for Scheduling Job Shops,'' Annals of Operations Research, Vol. 17, (1989), 233-248.

87

L. F. Martins, S. E. Shreve, and H. M. Soner, ``Heavy Traffic Convergence of a Controlled Multiclass Queuing System," SIAM J. Contr. Optim., Vol. 34, (1996), 2133-2171.

88

M. D. Mesarovic, D. Macko, and Y. Takahara, Theory of Multilevel Hierarchical Systems, Academic, New York, NY, 1970.

89

F. Modigliani and F. Hohn, ``Production Planning Over Time and the Nature of the Expectation and Planning Horizon", Econometrica, Vol. 23, (1955), 46-66.

90

R. Nagi, Design and Operation of Hierarchical Production Management Systems, PH.D. Thesis, System Research Center, University of Maryland, Baltimore, MD, 1991.

91

M.-T. Nguyen, Singular Perturbations in Deterministic and Stochastic Hybrid Control Systems: An Averaging Approach, Doctoral Dissertation, University of South Australia, Adelaide, Australia, 1999.

92

M.-T. Nguyen and V. Gaitsgory, `` Asymptotic Optimization for a Class of Nonlinear Stochastic Hybrid Systems on Infinite Time Horizon", Proceedings of the 1997 American Control Conference, 3587-3591.

93

R. G. Phillips and P. Koktovic, ``A Singular Perturbation Approach to Modeling and Control of Markov Chains,'' IEEE Trans. Automatic Control, Vol. AC-26, (1981), 1087-1094.

94

E. Presman, S. P. Sethi, and W. Suo, ``Optimal Feedback Production Planning in Stochastic Dynamic Jobshops," Mathematics of Stochastic Manufacturing Systems, Proceedings of the 1996 AMS-SIAM Summer Seminar in Applied Mathematics, G. Yin and Q. Zhang(Eds.), Lectures in Applied Mathematics, American Mathematical Society, Providence, RI, 1997a, 235-252.

95

E. Presman, S. P. Sethi, and W. Suo, ``Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop with Limited Buffers," Automatica, Vol. 33, (1997), 1899-1903.

96

E. Presman, S. P. Sethi, and H. Zhang, ``Optimal Production Planning in a N-Machine Flowshop with Long-Run Average Cost," Proceedings of the Indian Academy of Sciences (forthcoming), 1999a.

97

E. Presman, S. P. Sethi, and H. Zhang, ``Optimal Production Planning in a General Jobshop with Long-Run Average Cost," Working Paper, School of Management, The University of Texas at Dallas, 1999b.

98

E. Presman, S. P. Sethi, H. Zhang, and Q. Zhang, ``Optimality of Zero-Inventory Policies for an Unreliable Manufacturing System Producing Two Part Types", Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 4, (1998a), 485-496.

99

E. Presman, S. P. Sethi, and Q. Zhang, ``Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop,'' Proc. of 12th World Congress of International Federation of Automatic Control, Sydney, Australia, July 18-23 (1993).

100

E. Presman, S. P. Sethi, and Q. Zhang, ``Optimal Feedback Production Planning in a Stochastic N-Machine Flowshop," Automatic, Vol. 31, (1995), 1325-1332.

101

D. F. Rogers, J. R. Evans, R. D. Plante, and R. T. Wong, ``Aggregation and Disaggregation Techniques and Methodology in Optimization,'' Operations Research, Vol. 39, (1991), 553-582.

102

V. R. Saksena, J. O'Reilly, and P. Kokotovic, ``Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1983,'' Automatica, Vol. 20, (1984), 273-293.

103

C. Samaratunga, S. P. Sethi, and X. Y. Zhou, ``Computational Evaluation of Hierarchical Production Control Policies for Stochastic Manufacturing Systems,'' Operations Research, Vol. 45, (1997), 258-274.

104

S. P. Sethi, ``Some Insights into Near-Optimal Plans for Stochastic Manufacturing Systems," Mathematics of Stochastic Manufacturing Systems, G. Yin and Q. Zhang(Eds.), Lectures in Applied Mathematics, Vol. 33, American Mathematical Society, Providence, RI, 1997, 287-315.

105

S. P. Sethi, H. M. Soner, Q. Zhang, and J. Jiang, ``Turnpike Sets and Their Analysis in Stochastic Production Planning Problems,'' Mathematics of Operations Research, Vol. 17, (1992a), 932-950.

106

S. P. Sethi, W. Suo, M.I. Taksar and H. Yan, ``Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost," J. Discrete Event Dynamic Syst., Vol. 8, (1998), 37-54.

107

S. P. Sethi, W. Suo, M.I. Taksar and Q. Zhang, ``Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost," Journal of Optimization Theory and Applications, Vol. 92, (1997), 161-188.

108

S. P. Sethi, M. I. Taksar, and Q. Zhang, ``Capacity and Production Decisions in Stochastic Manufacturing Systems: An Asymptotic Optimal Hierarchical Approach,'' Prod. & Oper. Mgmt., Vol. 1, (1992b), 367-392.

109

S. P. Sethi, M. I. Taksar, and Q. Zhang, ``Hierarchical Decomposition of Production and Capacity Investment Decision in Stochastic Manufacturing Systems,'' International Transactions in Operations Research, Vol. 1, (1994a), 435-451.

110

S. P. Sethi and G. L. Thompson, ``Simple Models in Stochastic Production Planning,'' In Applied Stochastic Control in Econometrics and Management Science, Bensoussan, A., Kleindorfer, P. and Tapiero, C. (eds.). North-Holland, Amsterdam, (1981a), 295-304.

111

S. P. Sethi and G. L. Thompson, Optimal Control Theory: Applications to Management Science, Martinus Nijhoff Publishing, Boston, MA, 1981b.

112

S. P. Sethi, H. Yan, Q. Zhang, and X. Y. Zhou, ``Feedback Production Planning in a Stochastic Two Machine Flow Shop: Asymptotic Analysis and Computational Results,'' Int. J. Production Econ., Vol. 30-31, (1993), 79-93.

113

S. P. Sethi and H. Zhang, ``Hierarchical Production Planning in a Stochastic Manufacturing Systems with Long-Run Average Cost: Asymptotic Optimality," Stochastic Analysis, Control, Optimization and Applications, A Volume in Honor of W. H. Fleming, eds. W. McEneany, Y. Yin, and Q. Zhang, Birkhäuser, Boston, 1998.

114

S. P. Sethi and H. Zhang, ``Average-Cost Optimality of Kanban Policies for a Stochastic Flexible Manufacturing System," International Journal on Flexible Manufacturing Systems, Vol. 11, (1999), 213-224.

115

S. P. Sethi, H. Zhang and Q. Zhang, ``A Note on Optimal Production Rates in a Deterministic Two-Product Manufacturing System", Working Paper, School of Management, The University of Texas at Dallas, 1996.

116

S. P. Sethi, H. Zhang and Q. Zhang, ``Hierarchical Production Control in a Stochastic Manufacturing System with Long-Run Average Cost," Journal of Mathematical Analysis and Applications Vol. 214, (1997), 151-172.

117

S. P. Sethi, H. Zhang and Q. Zhang, ``Minimum Average Cost Production Planning in Stochastic Manufacturing Systems", Mathematical Models and Methods in Applied Sciences, Vol. 8, (1998), 1252-1276.

118

S. P. Sethi, H. Zhang and Q. Zhang, ``Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost," Working Paper, School of Management, The University of Texas at Dallas, 1999a.

119

S. P. Sethi, H. Zhang and Q. Zhang, ``Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost," Working Paper, School of Management, The University of Texas at Dallas, 1999b.

120

S. P. Sethi, H. Zhang and Q. Zhang, ``Hierarchical Production Planning in a Stochastic N-Machine Flowshop with Limited Buffers," Journal of Mathematical Analysis and Applications (to appear), 1999c.

121

S. P. Sethi, H. Zhang and Q. Zhang, ``Hierarchical Production Planning in a Stochastic Jobshop with Limited Buffers," Working Paper, School of Management, The University of Texas at Dallas, 1999d.

122

S. P. Sethi and Q. Zhang, ``Asymptotic Optimality in Hierarchical Control of Manufacturing Systems under Uncertainty: State of the Art," Operations Research Proceedings 1990, (W. Buehler, G. Feichtinger, R. Hartl, F. Radermacher, and P. Staehly, Eds.), Springer-Verlag, Berlin, (1992a), 249-263.

123

S. P. Sethi and Q. Zhang, ``Multilevel Hierarchical Controls in Dynamic Stochastic Marketing-Production Systems," Proc. of 31st IEEE CDC, Tucson, AZ, Dec. 16-18, (1992b), 2090-2095.

124

S. P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhäuser Boston, Cambridge, MA, 1994a.

125

S. P. Sethi and Q. Zhang, ``Hierarchical Production Planning in Dynamic Stochastic Manufacturing Systems: Asymptotic Optimality and Error Bounds," Journal of Mathematics Analysis and Applications, Vol. 181, (1994b), 285-319.

126

S. P. Sethi and Q. Zhang, ``Asymptotic Optimal Controls in Stochastic Manufacturing Systems with Machine Failures Dependent on Production Rates," Stochastics and Stochastics Reports, Vol. 48, (1994c), 97-121.

127

S. P. Sethi and Q. Zhang, ``Multilevel Hierarchical Decision Making in Stochastic Marketing-Production Systems," SIAM J. Contr. Optim., Vol. 33, (1995a), 528-563.

128

S. P. Sethi and Q. Zhang, ``Hierarchical Production and Setup Scheduling in Stochastic Manufacturing Systems," IEEE Trans. Auto. Contr., Vol. 40, (1995b), 924-930.

129

S. P. Sethi and Q. Zhang, and X. Y. Zhou, ``Hierarchical Controls in Stochastic Manufacturing Systems with Machines in Tandem," Stochastics and Stochastics Reports, Vol. 41, (1992a), 89-118.

130

S. P. Sethi, Q. Zhang, and X. Y. Zhou, ``Hierarchical Production Planning in a Stochastic Flowshop with a Finite Internal Buffer," Proc. of 31st IEEE Conference on Decision and Control, Tucson, AZ, December 16-18, (1992b), 2074-2079.

131

S. P. Sethi, Q. Zhang, and X. Y. Zhou, ``Hierarchical Controls in Stochastic Manufacturing Systems in th Convex Costs," Journal of Optimization Theory and Applications, Vol. 80, (1994), 303-321.

132

S. P. Sethi, Q. Zhang, and X. Y. Zhou, ``Hierarchical Production Controls in a Stochastic Two-Machine Flowshop with a Finite Internal Buffer," IEEE Trans. on Robotics and Automation, Vol. 13, (1997), 1-13.

133

S. P. Sethi and X. Y. Zhou, ``Stochastic Dynamic Job Shops and Hierarchical Production Planning," IEEE Trans. Auto. Contr., Vol. 39, (1994), 2061-2076.

134

S. P. Sethi and X. Y. Zhou, ``Optimal Feedback Controls in Deterministic Dynamic Two-Machine Flowshops," Operations Research Letters, Vol. 19, (1996a), 225-235.

135

S. P. Sethi and X. Y. Zhou, ``Asymptotic Optimal Feedback Controls in Stochastic Dynamic Two-Machine Flowshops," in Recent Advances in Control and Optimization of Manufacturing Systems, Lecture Notes in Control and Information Science, Vol. 214, G. Yin and Q. Zhang (eds.), Springer-Verlag, New York, NY, 1996b, 203-216.

136

A. Sharifnia, ``Production Control of a Manufacturing System with Multiple Machine States," IEEE Trans. Auto. Contr. Vol. AC-33, (1988), 620-625.

137

A. Sharifnia, M. Caramanis, and S. B. Gershwin, ``Dynamic Setup Scheduling and Flow Control in Manufacturing Systems," J. Discrete Event Dynamic Syst., Vol. 1, (1991), 149-175.

138

P. Shi, E. Altman, and V. Gaitsgory, ``On Asymptotic Optimization for a class of Nonlinear Stochastic Hybrid Systems", Mathematical Methods of Oper. Res., Vol. 47, (1998), 229-315.

139

H. A. Simon, ``The Architecture of Complexity," Proc. of the American Philosophical Society, Vol. 106, (1962), 467-482; reprinted as Chapter 7 in Simon, H.A., The Sciences of the Artificial, 2nd Ed., The MIT Press, Cambridge, MA, 1981.

140

M. G. Singh, Dynamical Hierarchical Control, Elsevier, New York, NY, 1982.

141

N. J. Smith and A. P. Sage, "An Introduction to Hierarchical Systems Theory," Computers and Electrical Engineering, Vol. 1, (1973), 55-72.

142

H. M. Soner, ``Optimal Control with State Space Constraints II," SIAM J. Contr. Optim, Vol. 24, (1986), 1110-1122.

143

H. M. Soner, ``Singular Perturbations in Manufacturing Systems," SIAM J. Contr. Optim., Vol. 31, (1993), 132-146.

144

A. Y. Sprzeuzkouski, ``A Problem in Optimal Stock Management", Journal of Optimization Theory and Applications, Vol. 1, (1967), 232-241.

145

N. Srivatsan, Synthesis of Optimal Policies in Stochastic Manufacturing Systems, Ph.D. Thesis, MIT, Operations Research Center, Cambridge, MA, 1993.

146

N. Srivatsan, S. Bai, and S. B. Gershwin, ``Hierarchical Real-Time Integrated Scheduling of a Semiconductor Fabrication Facility," in Computer-Aided Manufacturing/Computer-Integrated Manufacturing, Part II of Vol. 61 in the Series Control and Dynamic Systems, Leondes, C.T.(ed.) Academic Press, New York, (1994), 197-241.

147

N. Srivastsan and Y. Dallery,``Partial Characterization of Optimal Hedging Point Polices in Unreliable Two-Part-Type Manufacturing Systems," Operations Research, Vol 46, (1998), 36-45.

148

N. Srivatsan and S. B. Gershwin, ``Selection of Setup Times in a Hierarchically Controlled Manufacturing System," Proc. of 29th IEEE-CDC, Honolulu, HI, 1990, 575-581.

149

H. Stadtler, Hierarchische Produktionsplanung bei Losweiser Fertigung, Physica-Verlag, Heidelberg, Germany, 1988.

150

M. Switalski, Hierarchische Produktionsplanung, Physica-Verlag, Heidelberg, Germany, 1989.

151

G. L. Thompson and S. P. Sethi, ``Turnpike Horizons for Production Planning,'' Management Science. Vol. 26, 3, (1980), 229-241.

152

G. L. Thompson, S. P. Sethi, and J.-T. Teng, ``Strong Planning and Forecast Horizons for a Model with Simultaneous Price and Production Decisions," European Journal of Operational Research, Vol. 16, (1984), 378-388.

153

R. Uzsoy, C. Y. Lee, and L. Martin-Vega, ``A Review of Production Planning and Scheduling of Models in the Semiconductor Industry, Part II: Shop Floor Control", IIE Transactions on Scheduling and Logistic, Vol. 26, (1996).

154

G. J. Van Ryzin, X. C. Lou, and S. B. Gershwin, ``Production Control for a Tandem Two-Machine System," IIE Transactions, Vol. 25, (1993), 5-20.

155

M. H. Veatch, Queuing Control Problems for Production/Inventory Systems, Ph.D. Thesis, MIT, Operations Research Center, Cambridge, MA, 1992.

156

M. H. Veatch and M. C. Caramanis, `` Optimal Average Cost Manufacturing Flow Controllers: Convexity and Differentiability," IEEE Trans. Auto. Contr., Vol. 44, (1999), 779-783.

157

A. F. Veinott, ``Production Planning with Convex Costs: A Parametric Study", Management Science, Vol. 10, (1964), 441-460.

158

D. Vermes, Optimal Control of Piecewise Deterministic Markov Processes, Stochastics, Vol. 14, 1985, 165-207.

159

J. Violette, Implementation of a Hierarchical Controller in a Factory Simulation, M.S. Thesis, MIT Department of Aeronautics and Astronautics, Cambridge, MA, 1993.

160

J. Violette and S. B. Gershwin, ``Decomposition of Control in a Hierarchical Framework for Manufacturing Systems," Proc. of the 1991 Automatic Control Conference, Boston, MA, (1991), 465-474.

161

L. Wein, ``Optimal Control of a Two-Station Brownian Network," Mathematics of Operations Research, Vol. 15, (1990), 215-242.

162

P. Whittle, Risk-Sensitive Optimal Control, Wiley, New York, 1990.

163

X. L. Xie, ``Hierarchical Production Control of a Flexible Manufacturing System," Applied Stochastic Models and Data Analysis, Vol. 7, (1991), 343-360.

164

H. Yan, S. Lou, S. P. Sethi, A. Gardel, and P. Deosthali, ``Testing the Robustness of Two-Boundary Control Policies in Semiconductor Manufacturing", IEEE Transactions on Semiconductor Manufacturing, Vol. 9, (1996), 285-288.

165

H. Yan, G. Yin, and S. Lou, ``Using Stochastic Optimization to Determine Threshold Values for Control of Unreliable Manufacturing Systems", Journal of Optimization Theory and Applications, Vol. 83, (1994), 511-539.

166

G. Yin and Q. Zhang, Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Springer-Verlag, New York, NY, 1997.

167

Q. Zhang, `` Risk Sensitive Production Planning of Stochastic Manufacturing Systems: A Singular Perturbation Approach," SIAM J. Contr. Optim., Vol. 33, (1995), 498-527.