Joint Order Fulfillment and Inventory Management in Assemble-to-Order Generalized W Systems

This paper characterizes joint order fulfillment and inventory policies for assemble-to-order generalized W systems, in which k products are assembled from a common component and k product-specific (dedicated) components. We consider a periodic-review system and focus on nested fulfillment policies, in which orders are fulfilled in decreasing order of profit margins. We prove that the optimal fulfillment policy of a two-product W system is nested. For systems with more than two products, although nested policies may not be optimal in general, we identify a sufficient condition for the optimal policy to be nested, and furthermore, we show that a nested policy is asymptotically optimal in a high-demand regime. Based on these results, we develop an asymptotically optimal strategy for the joint fulfillment and inventory decision under which the policy for demand fulfillment is static nested and that for inventory procurement is of the newsvendor type. In addition, we derive insights regarding the interactions between the component inventories and find that although the inventories of the common component and a particular dedicated component are complementary, those of different dedicated components may not be substitutable.