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Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands

  • A. Federgruen

    (Columbia University)

  • H. Groenevelt

    (Columbia University)

  • H. C. Tijms

    (Vrije Universiteit, Amsterdam, The Netherlands)

In many practical applications or 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.

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Article provided by INFORMS in its journal Management Science.

Volume (Year): 30 (1984)
Issue (Month): 3 (March)
Pages: 344-357

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Handle: RePEc:inm:ormnsc:v:30:y:1984:i:3:p:344-357
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