Optimal PHP production of multiple part-types on a failure-prone machine with quadratic buffer costs

We consider a single, failure-prone machine, producing multiple part-types The objective is to minimize the expected sum of quadratic buffer costs. In general, the optimal solution to this problem is unknown. However, by restricting the allowable set of control policies to the class of prioritized hedging point (PHP) policies, we are able to determine simple, analytical expressions for the optimal hedging points. We also provide some results for choosing the optimal priority ordering.