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

• Published in: Management science Vol. 30; no. 3; pp. 344 - 357
• Main Authors: Federgruen, A, Groenevelt, H, Tijms, H. C
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.03.1984; Institute of Management Sciences; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Algorithms; Approximation; Average cost; Carrying costs; compound Poisson demand processes; coordinated replenishments; Cost control; Decision making models; Decision theory; Decomposition; Excess demand; Heuristic; Heuristics; Integers; Inventories; Inventory control; Inventory management; Lead; Lead compounds; multi-item inventory systems; Order quantity; Poisson process; policy-iteration algorithm; Random variables; service level constraint
• DOI: 10.1287/mnsc.30.3.344
• ISSN: 0025-1909

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.