Component inventory costs in an assembly problem with uncertain supplies lead-times

This paper presents a generic study of inventory costs in a factory stockroom that supplies component parts to an assembly line. Specifically, it is concerned with the increase in component inventories due to uncertainty in supplier lead-times, and the fact that several different components must be present before assembly can begin. It is assumed that the suppliers of the various components are independent, that the suppliers’ operations are in statistical equilibrium, and that the same amount of each type of component is demanded by the assembly line each time a new assembly cycle is scheduled to begin. The paper uses, as a measure of inventory cost, the expected time for which an order of components must be held in the stockroom from the time it is delivered until the time is consumed by the assembly line. The work reveals the effects of supplier lead-time variability, the number of different types of components, and their desired service levels, on the inventory cost. In addition, under the assumptions that inventory holding costs and the cost of delaying assembly are linear in time, it studies optimal ordering policies and presents an interesting characterization that is independent of the supplier lead-time distributions.