A note on assemble-to-order systems with batch ordering

We study an assemble-to-order inventory system. The stocks are held for components, with final products assembled only when customer orders are realized. Customer orders form a multivariate compound Poisson process, component replenishment leadtimes are constant, and demands in excess of inventory on hand are backlogged. The component inventories are controlled by (R, nQ) policies. We show that under certain general conditions the inventory position vector has a uniform equilibrium distribution. This result generalizes the corresponding single-item theory considerably. It allows us to express the key performance measures of the system such as order fill rates and average order-based backorders, as the averages of their counterparts in the base-stock systems.