We extend the theory of the exogenous and sequential supply systems to a framework that includes multi-stage assembly systems and multiple products. We provide a uniform and exact treatment to various material flow topologies such as serial, assembly and distribution systems with either a single product or multiple products sharing the common components. Recursive equations of the backorder delays are derived for every item at all stages in the supply chains, which allow us to characterize the intricate correlations in multi-product and multi-stage assembly systems.

Based on the recursive equations, we present new system properties and insights into the optimal safety stock positions. To achieve the numerical efficiencies, we propose approximations and specify conditions under which the approximations may be applied. Finally we propose algorithms based on dynamic programming to determine the stock levels at each stage of the supply chains so that the system-wide inventory cost is minimized while the service requirements of the external customers are satisfied.