## Awi Federgruen

*Infinite horizon strategies for replenishment systems with a general pool of suppliers*

Coauthor(s): Nan Yang.

**Abstract:**

We consider a general infinite horizon inventory control model which 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 criterion, and characterize its structure. Assuming each period's inventory level distribution can be approximated as an Normal, we develop an efficient solution method identifying additional structural properties. Finally, we identify a simple class of heuristic policies which come close to being optimal.

**Source:** *Working paper*

**Exact Citation:**

Federgruen, Awi, and Nan Yang. "Infinite horizon strategies for replenishment systems with a general pool of suppliers." Working paper, Columbia Business School, January 2010.

**Date:**
1
2010