Enforcing service-level constraints in supply chains with assembly operations

In this paper we study a feedforward supply network that involves assembly operations. Demand is met from the most downstream stage and all stages operate subject to capacity constraints. We analyze a base-stock production policy where each stage has knowledge of its local inventory and of the inventory level of all its downstream stages. We compute optimal stock levels which minimize inventory costs and maintain stockout probabilities below given desirable levels (service-level constraints). Our approach consists of developing large deviations approximations for inventory costs and service level constraints and formulating the stock level selection problem as a nonlinear programming problem which can be solved using standard techniques. It results in huge computational savings when compared to exhaustive search using simulation. Our distributional assumptions are general enough to include temporal dependencies in the demand and production processes. We claim that such distributional information is critical in making inventory control decisions.