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

A. Federgruen, H. Groenevelt and Henk Tijms
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A. Federgruen: Columbia University
H. Groenevelt: Columbia University

Management Science, 1984, vol. 30, issue 3, 344-357

Abstract: 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.

Keywords: multi-item inventory systems; coordinated replenishments; compound Poisson demand processes; service level constraint; policy-iteration algorithm (search for similar items in EconPapers)
Date: 1984
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