Infinite Horizon Strategies for Replenishment Systems with a General Pool of Suppliers

We consider a general infinite horizon inventory control model that combines demand and supply risks and the firm's ability to mitigate the supply risks by diversifying its procurement orders among a set of N potential suppliers. Supply risks arise because only a random percentage of any given replenishment order is delivered as useable units. The suppliers are characterized by the price they charge and the distribution of their yield factor. Assuming unsatisfied demand is backlogged, the firm incurs, as in standard inventory models, three types of costs: (i) procurement costs, (ii) inventory carrying costs for units carried over from one period to the next, and (iii) backlogging costs. We establish the existence of an optimal stationary policy, under both the long-run discounted and average cost criteria, and characterize its structure. Assuming each period's inventory level distribution can be approximated as a normal, we develop an efficient solution method identifying additional structural properties. Finally, we identify a simple class of heuristic policies that come close to being optimal.