Analysis of a single-stage, single-product, stochastic, MRP-controlled assembly system

This paper models a single-stage, single-product, stochastic assembly system, operating according to a Materials Requirements Planning controlled ordering philosophy. It deals explicitly with the underlying stochastic process that describes the end-product inventory position, enabling production lead times to be treated as independent and generally distributed random variables. The inventory position process is identified as a Markov renewal process, and this structure is exploited to determine system performance measures such as average inventory level, average backorder level, and the probability distribution of the end-product inventory position. An example, which demonstrates the type of analysis possible, focuses on quantifying the effect of kitting on the availability of end-products.