Optimal control structure of an unreliable manufacturing system with random demands

The optimal service control of an unreliable manufacturing system with random demands is discussed. The system can product many part types The objective is to find an optimal policy to minimizing the expected discounted inventory and backlog cost. Structural properties of the optimal control are investigated. It is shown that the optimal policy is of switching structure. For production of one type of part, the optimal control is a threshold policy. For production of two types of part, the optimal control can be described by three monotone switching curves and its asymptote properties are derived. Numeric examples are given to demonstrate the results.