Hierarchical Decision Making in Stochastic Manufacturing Systems: (Systems & Control: Foundations & Applications)

Most manufacturing systems are large, complex, and subject to uncertainty. Obtaining exact feedback policies to run these systems is nearly impossible, both theoretically and computationally. It is a common practice, therefore, to manage such systems in a hierarchical fashion. This book articulates a theory that shows that hierarchical decision making in the context of a goal-seeking manufacturing system can lead to near optimization of its objective. The approach in this book considers manufacturing systems in which events occur at different time scales. For example, changes in demand may occur far more slowly than breakdowns and repairs of production machines. This suggests that capital expansion decisions that respond to demand are relatively longer term than those decisions regarding production. Thus, long-term decisions such as those dealing with capital expansion can be based on the average existing production rapacity, and can be expected to be nearly optimal even though the short-term capacity fluctuations are ignored. Having the long-term decisions in hand, one can then solve the simpler problem of obtaining production rates. Increasingly complex and realistic models of manufacturing systems with failure-prone machines facing uncertain demands are formulated as stochastic optimal control problems. Partial characterization of their solutions is provided when possible along with their hierarchical decomposition based on event frequencies. In the latter case, multilevel decisions are constructed in the manner described above and these decisions are shown to be asymptotically optimal as the average time between successive short-term events becomes much smaller than that between successive long-term events. Much attention is given to establish that the order of deviation of the cost of the hierarchical solution from the optimal cost is small. The striking novelty of the approach is that this is done without solving for the optimal solution, which as stated earlier is an insurmountable task. This approach presents a paradigm in convex production planning, whose roots go back to the classical work of Arrow, Karlin and Scarf (1958). It also represents a new research direction in control theory. Finally, the material covered in the book cuts across the disciplines of Operations Management, Operations Research, System and Control theory, Industrial Engineering, Probability and Statistics, and Applied Mathematics. It is anticipated that the book would encourage development of new models and techniques in these disciplines.

Table of Contents:
I. Introduction and Models of Manufacturing Systems.- 1. Concepts of hierarchical decision making.- 2. Models of manufacturing systems.- II. Optimal Control of Manufacturing Systems: Existence and Characterization.- 3. Optimal control of parallel machine systems.- 4. Optimal control of dynamic flowshops.- III: Asymptotic Optimal Controls.- 5. Hierarchical controls in systems with parallel machines.- 6. Hierarchical controls in dynamic flowshops.- 7. Hierarchical controls in dynamic jobshops.- 8. Hierarchical production and setup scheduling in a single machine system.- 9. Hierarchical feedback controls in two-machine flowshops.- IV: Multilevel Hierarchical Decisions.- 10. A production and capacity expansion model.- 11. Production-marketing systems.- V: Computations and Conclusions.- 12. Computations and evaluation of hierarchical controls.- 13. Further extensions and open research problems.- VI: Appendices.- A. Finite state Markov chains.- B. Martingale problems, tightness, and Skorohod representation.- C. Rate of convergence of Markov chains.- D. Control-dependent Markov chains.- E. Convergence of Markov chains with two parameters.- F. Convex functions.- G. Viscosity solutions of HJB equations.- H. Value functions and optimal controls.- I. A review of relevant graph theory.- J. Miscellany.- Author index.- Copyright permissions.

Review :
"This monograph is both a well-prepared report about brand-new results of recent research and a very nicely and carefully written (graduate) textbook on the field of stochastic manufacturing systems. It is recommendable to operations researchers and system theorists as well as to applied mathematicians." --Optimization "A truly remarkable book, in which Sethi and Zhang have contributed enormously to the area of hierarchical controls in manufacturing. It is strongly recommended to operations researchers, industrial engineers, system and control theorists, applied mathematicians, and specialists in operations management." -- Journal of Discrete Event Dynamic Systems "This book is clearly intended for an audience that is well versed in dynamic programming and finite state Markov processes. It would be well suited for researchers and graduate students in operations research, systems and control theory, and applied mathematics. Sethi and Zhang provide a very clearly written book that fills a gap in the research on hierarchical control of manufacturing systems by synthesizing research that was previously available only in research journals into a well-organized single volume." -- Interfaces "Suresh Sethi has clearly made a series of important extensions to the treatment of hierarchical systems and applications to management science problems, and the book with Zhang is an impressive piece of work." -- Herbert A. Simon, Carnegie Mellon University "The book is clearly written for operation researchers, system and control theorists and applied mathematicians." -- Mathematical Reviews "Clear descriptions are followed by rigorous mathematical treatments. The bibliography is extensive and good...The book is a valuable progress report." -- Computing Reviews "The book is recommended to anybody who has an interest in applied stochastic processes or manufacturing problems." -- Short Book Reviews