Hierarchical controls in systems with parallel machines

In this chapter we consider a manufacturing system which consists of a single machine or a number of parallel machines that are subject to breakdown and repair. The problem of the system is to obtain the rate of production over time in order to meet the demand at the minimum expected discounted cost of production and surplus over the infinite horizon. An exact optimal solution of the problem is quite complex and difficult to obtain. Therefore, we resort to obtaining an approximately optimal solution by using a hierarchical approach.