Analysis of the steady state probability distribution of a manufacturing system under the prioritised hedging point control policy

In order to evaluate the average production cost of a multi-product-type, multi-stage and multi-parallel-machine manufacturing system (denoted as mP/mS/mM), one of the effective ways is to obtain its steady-state probability distribution. Because the two-product-type and multi-parallel-machine system that demand backlog is not allowed can be considered as a basic building block of the mP/mS/mM system, we begin by investigating the method of obtaining its steady-state probability distribution under the prioritised hedging point control policy. Although the shape of the distribution domains of the work-in-process (WIP) levels influences the steady-state probability balance equations, we develop a unified form of the marginal probability balance equations for all the possible shapes of distribution domains, which can be used to calculate the marginal probability distribution for each product type for the two-product-type and multi-parallel-machine system. Furthermore, we extend this analysis method to both the multiple-product-type, multi-parallel-machine, and single-stage system and the more complex mP/mS/mM system, and propose a method to obtain their approximate marginal probability distributions of the WIP levels. Finally, numerical experiments are conducted to verify the accuracy of the proposed method of analysing the steady-state probability distribution of an mP/mS/mM system.