Independence of the hedging points in PHP control policy

For the control of single machine and multiple part-types manufacturing systems, the prioritized hedging point (PHP) policy is often used. In this paper, the probability distribution of the system states under this control is analysed. Unlike the work by Shu and Perkins (2001), where the maximum production rates for all part-types are identical, we deal with the situation that the maximum production rates for various part-types are different from each other. For this situation, we obtain the independence property of the PHP policy, that is, the marginal probability density function of the production surplus of a specific part-type only relies on the hedging point of itself, but does not depend on the hedging points of other part-types. On the basis of this property, the problem of optimizing the hedging points of the PHP policy can be solved by dividing the single machine and multiple part-types system into a series of equivalent single machine and single part-type systems, the closed form of whose optimal hedging point is known and can be applied directly to optimize the hedging points of the PHP policy.