Average-Cost Control of Stochastic Manufacturing Systems

by Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing

• ISBN13: 9780387219479
• ISBN10: 0387219471
• Format: Hardcover
• Copyright: 2005-05-15
• Publisher: Springer Verlag

Summary

This book articulates a new theory that shows that hierarchical decision making can in fact lead to a near optimization of system goals. The material in the book cuts across disciplines. It will appeal to graduate students and researchers in applied mathematics, operations management, operations research, and system and control theory.

Table of Contents

Preface	vii
Notation	xiii
Part I: Introduction and Models of Manufacturing Systems	1	(20)
Concept of Near-Optimal Control	3	(8)
Introduction	3	(1)
A Brief Review of the Related Literature	4	(3)
Plan of the Book	7	(4)
Models of Manufacturing Systems	11	(10)
Introduction	11	(1)
A Parallel-Machine, Single Product Model	12	(3)
A Parallel-Machine, Multiproduct Model	15	(1)
A Single Product Dynamic Flowshop	16	(1)
A Dynamic Jobshop	17	(4)
Part II: Optimal Control of Manufacturing Systems: Existence and Characterization	21	(122)
Optimal Control of Parallel-Machine Systems	23	(44)
Introduction	23	(2)
Problem Formulation	25	(3)
Estimates for Discounted Cost Value Functions	28	(11)
Verification Theorem	39	(5)
Existence and Characterization of Optimal Policy	44	(4)
Turnpike Set Analysis	48	(5)
Multiproduct Systems	53	(11)
Notes	64	(3)
Optimal Control of Dynamic Flowshops	67	(30)
Introduction	67	(1)
Problem Formulation	68	(3)
Estimates for Discounted Cost Value Functions	71	(6)
Verification Theorem and HJBDD Equations	77	(7)
Two-Machine Flowshop with Finite Internal Buffer	84	(10)
Notes	94	(3)
Optimal Controls of Dynamic Jobshops	97	(28)
Introduction	97	(2)
A Graph-Theoretic Framework and Problem Formulation	99	(11)
Estimates for Discounted Cost Value Functions	110	(6)
Verification Theorem	116	(7)
Notes	123	(2)
Risk-Sensitive Control	125	(18)
Introduction	125	(1)
Problem Formulation	126	(2)
HJB Equations	128	(12)
Verification Theorem	140	(2)
Notes	142	(1)
Part III: Near-Optimal Controls	143	(96)
Near-Optimal Control of Parallel-Machine Systems	145	(26)
Introduction	145	(1)
Problem Formulation	146	(3)
The Limiting Control Problem	149	(2)
Convergence of the Minimum Average Expected Cost	151	(6)
Asymptotic Optimal Controls	157	(7)
Parallel-Machine Systems without Attrition	164	(6)
Notes	170	(1)
Near-Optimal Control of Dynamic Flowshops	171	(28)
Introduction	171	(1)
Problem Formulation	172	(4)
The Limiting Control Problem	176	(2)
Convergence of the Minimum Average Expected Cost	178	(17)
Construction of a Near-Optimal Control	195	(3)
Notes	198	(1)
Near-Optimal Controls of Dynamic Jobshops	199	(28)
Introduction	199	(1)
The Optimization Problem	199	(5)
The Limiting Control Problem	204	(2)
Convergence of the Minimum Average Expected Cost	206	(17)
Construction of a Near-Optimal Control	223	(3)
Notes	226	(1)
Near-Optimal Risk-Sensitive Control	227	(12)
Introduction	227	(1)
Problem Formulation	228	(1)
The Limiting Problem	229	(8)
Notes	237	(2)
Part IV: Conclusions	239	(8)
Further Extensions and Open Research Problems	241	(6)
Introduction	241	(1)
Multilevel Systems	242	(1)
Asymptotic Optimal Feedback Controls	242	(1)
Robust Controls	243	(1)
General Systems	244	(1)
Final Thoughts	244	(3)
Part V: Appendices	247	(58)
A Finite State Markov Chains	249	(4)
B Convergence and Error Estimates of Markov Chains	253	(30)
C Convex Sets and Functions	283	(4)
D Viscosity Solutions of HJB Equations	287	(8)
E Discounted Cost Problems	295	(6)
F Miscellany	301	(4)
References	305	(12)
Author Index	317	(2)
Subject Index	319	(2)
Copyright Permissions	321