Corrected Diffusion Approximations for a Multistage Production-Inventory System

We analyze a multistage inventory system with limited production capacity facing stochastic demands. Each node follows a periodic-review base-stock policy for echelon inventory: in each period, each node attempts to produce enough material to restore cumulative down-stream inventory to a fixed target level. We develop approximations to the key measures of interest (average inventories, average backorders, and service levels) by simultaneously letting the mean demand approach the system's bottleneck capacity and letting the base-stock level for finished goods increase without bound. Using a method of Siegmund, we thus obtain diffusion limits with higher-order correction terms. A numerical example suggests that the correction terms can substantially improve the accuracy of the approximations.