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

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 b...

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Bibliographic Details
Published inManagement science Vol. 30; no. 3; pp. 344 - 357
Main Authors Federgruen, A, Groenevelt, H, Tijms, H. C
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.03.1984
Institute of Management Sciences
Institute for Operations Research and the Management Sciences
SeriesManagement 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
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Summary: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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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.30.3.344