Structural properties of optimal production controllers in failure-prone manufacturing systems

A failure-prone manufacturing system with one part-type and multiple machine states is considered. Each machine state has a given production capacity but is associated with several possible failure stages. Although transition times between failure stages are assumed exponential, the existence of multiple stages within each machine state allows failure times to have a distribution more general than the exponential distribution. For such a system, it is shown that the well-known hedging point policy minimizes inventory and backlog costs for a constant demand rate. The value of the optimal hedging points is now a function of failure stage as well as machine state. By ordering machine states according to increasing distance from the zero capacity state and failure stages according to distance from the capacity reduction transition, we show that hedging points increase monotonically when the machine state number decreases or the stage number increases. This can be intuitively interpreted as follows: the closer to the zero capacity state the system is, the larger the hedging point should be. This structural property of the optimal control is very useful in searching for the optimal control or designing near-optimal controls