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.