NOVEL STOCHASTIC PROGRAMMING FORMULATIONS FOR ASSEMBLE-TO-ORDER SYSTEMS

Abstract

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.