Supply Performance in Multi-Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

Abstract

In this article, we study the performance of multi-echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end-product demand and spare parts (subassemblies) demand. The multi-echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi-echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation-based inventory optimization approach is developed to search for the best base-stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample-path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on-hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.