New necessary and sufficient condition for the irreducibility of joint inventory positions in an assemble-to-order system

Abstract

When joint inventory positions in an assemble-to-order system are irreducible, it has been proved that the evaluation on order-based backorders can be based on a set of systems under the base stock policy. We provide a new necessary and sufficient condition for the irreducibility of the joint inventory positions where the item inventory is controlled by an (r,nQ) policy. The computation complexity of applying this new condition is much lower than that of verifying the previous condition.