Managing two-stage serial inventory systems under demand and supply uncertainty and customer service level requirements

We consider a two-echelon serial inventory system with demand and supply uncertainty, non-zero lead times for component procurement and end-product assembly, and a minimum customer service level requirement. We present two supply models which incorporate both quantity and timing uncertainty; these models correspond to current and proposed supply environments. Assuming that installation base-stock ordering policies are followed and that the demand distribution is quasi-concave, we show that the chance-constrained problem of determining optimal base-stock levels which minimize the total inventory investment ( cost-weighted stock levels) subject to a service constraint is a convex programming problem. We characterize the relation between the optimal base-stock levels of the component and the end-product. We also illustrate how an optimal internal ( component) service level can be computed, which permits decomposition of the two-stage serial system into two coordinated single-echelon systems. Computational experiments illustrate insights on the effects of supply uncertainty and other problem parameters on stock-positioning in a two-echelon serial system. In particular, we evaluate the benefits of switching from one supply environment to another.