We study a periodic review assemble-to-order (ATO) system introduced by Akcay and Xu (2004) which jointly optimizes the base stock levels and the component allocation with an independent base stock policy and a first-come- first-served allocation rule. The formulation is a non-smooth and thus theoretically and computationally challenging. In their computational experiments, Akcay and Xu (2004) modified the right hand side of the inventory availability constraints by substituting linear functions for piece-wise linear ones. This modification may have a significant impact on low budget levels. The optimal solutions obtained via the original formulation, i.e., the formulation without modification, include zero base stock levels for some components and thus indicate a bias against component commonality. We study the impact of component commonality on periodic review ATO systems. We show that lowering component commonality may yield a higher type-II service level. The lower degree of component commonality is achieved via separating inventories of the same component for different products. We substantiate this property via computational and theoretical approaches. We show that for low budget levels the use of separate inventories of the same component for different products can achieve a higher reward than with shared inventories. Finally, considering a simple ATO system with one component shared by two products, we characterize the budget ranges such that either separate or shared inventory component (i.e., component commonality) is beneficial. / Thesis / Doctor of Philosophy (PhD)

In the warehouse of a large cosmetics company, a mechanized order picker is restocked from nearby shelving, and the shelving is restocked from bulk storage, forming a three-tier inventory system. We consider such multi-tier inventory systems and determine the storage areas to which to assign items, and the quantities in which to store them, in order to minimize the total cost of picking items and restocking storage locations. With this research, we increase the number of inventory systems for which simple search algorithms find a provably near-optimal solution. The model and method were tested on data from the Avon Products distribution center outside Atlanta; the solution identified by the model reduced picking and restocking costs there by 20%. The sales forecasts of items stored in the warehouse may change, however, and new items will be introduced into the inventory system and others removed. To account for these changes, some warehouses may periodically reassign items to storage areas and recompute their storage quantities. These reassignment activities account for additional costs in the warehouse. The second focus of this research examines these costs over several time periods in a simple multi-tier inventory system. We develop heuristics to determine the storage areas to which to assign items and the quantities in which to store them in each time period, in order to minimize the total cost of picking items, restocking storage locations, and reassigning skus over multiple periods.