On component commonality for periodic review assemble-to-order systems

We study the value of component commonality in a periodic review assemble-to-order system, introduced by Akçay and Xu in 2004, where an independent base stock policy and a first-come-first-served allocation rule are used, and the base stock levels and the component allocation are optimized jointly. 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. In their computational experiments, Akçay and Xu 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 for low budget levels. The optimal solutions obtained via the original formulation; that is, without the modification, include zero base stock levels for some components and, thus, indicate a bias against component commonality. 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 could achieve a higher objective than with shared inventories. Finally, considering a simple assemble-to-order system consisting of one component shared by two products, we characterize the budget ranges such that the use of separate inventories is beneficial, as well as the budget ranges such that component commonality is beneficial.