Order-based cost optimization in assemble-to-order systems

We study a multi-item stochastic inventory system in which customers may order different but possibly overlapping subsets of items, such as a multiproduct assemble-to-order system. The goal is to determine the right base-stock level for each item and to identify the key driving factors. We formulate a cost-minimization model with order-based backorder costs and compare it with the standard single-item, newsvendor-type model with item-based backorder cost. We show that the solution of the former can be bounded by that of the latter with appropriately imputed parameters. Starting with this upper bound, the optimal base-stock levels of the order-based problem can be obtained in a greedy fashion. We also show that the optimal base-stock levels increase in replenishment lead times but may increase or decrease in lead-time variability and demand correlation. Finally, we devise closed-form approximations of the optimal base-stock levels to see more clearly their dependence on the system parameters.