Analysis of a multi‐component periodic review inventory system in an assembly environment

Inventory systems within production or distribution chains typically interact with preceding supply and successive demand processes. We observe that the more clearly the performance characteristics of an inventory system are described and communicated, the better the planning and configuration of the surrounding systems can be. This paper is thus dedicated to the analysis of a component inventory model that is typically found within multi‐level supply chain structures. Operating on a discrete time axis, we assume that lead times are discretely distributed, and may also depend on preceding occurrences. Customer demand for the components emerges from a single end product that requires all of the components, and whose demand per period is continuously i.i.d. The components are replenished according to a periodic review order‐up‐to (r, S ^[i]) policy, where r is common to all components and S ^[i] may be selected individually. Particularly, we discuss the modeling of the lead time process and give a detailed analysis of the delay time process versus the successive level of the supply chain. The analysis is exact and has not so far been conducted on the delay time of a comparable system. We have given special emphasis to elaborating the relevant formulae and computational approaches to a level at which they are ready to be computed.