One of the most important methods in dealing with the optimization of large, complex systems is that of hierarchical decomposition. The idea is to reduce the overall complex problem into manageable approximate problems or subproblems, to solve these problems, and to construct a solution of the original problem from the solutions of these simpler prob­ lems. Development of such approaches for large complex systems has been identified as a particularly fruitful area by the Committee on the Next Decade in Operations Research (1988) [42] as well as by the Panel on Future Directions in Control Theory (1988) [65]. Most manufacturing firms are complex systems characterized by sev­ eral decision subsystems, such as finance, personnel, marketing, and op­ erations. They may have several plants and warehouses and a wide variety of machines and equipment devoted to producing a large number of different products. Moreover, they are subject to deterministic as well as stochastic discrete events, such as purchasing new equipment, hiring and layoff of personnel, and machine setups, failures, and repairs.

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.