In many practical applications of multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.

Awi Federgruen, Henri Groenevelt, and H. C. Tijms
Journal Article
Publication Date
Management Science

Full Citation

Federgruen, Awi, Henri Groenevelt, and H. C. Tijms
. “Coordinated replenishments in a multi-item inventory system with compound Poisson demands.”
Management Science
, (March 01, 1984):