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European Journal of Operational Research
Volume 175, Issue 1, 16 November 2006, Pages 593-601
 
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doi:10.1016/j.ejor.2005.04.043    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2005 Elsevier B.V. All rights reserved.

Production, Manufacturing and Logistics

Inventory control with indivisible units of stock transfer

Roger M. HillCorresponding Author Contact Information, a, E-mail The Corresponding Author

aDepartment of Mathematical Sciences, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE, United Kingdom

Received 29 April 2004; 
accepted 21 April 2005. 
Available online 10 August 2005.

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Abstract

We consider an infinite horizon, single item inventory model with backorders and a fixed lead time. Demand is stationary stochastic and review is periodic. Inventory may only be replenished in multiples of a fixed package size q but demands may be of any size. Ordering costs are linear and combined holding and shortage costs can be expressed as a convex function of the inventory position. The control policy is defined as (sSq), where an order is placed if the inventory position falls to or below s and the order size is the largest multiple of q which results in the inventory position not exceeding S. The parameters s and S are restricted to be multiples of q. The objective is to find the control policy that minimizes the long run average cost per unit time. The optimal solution procedure requires renewal theory and a structured search. Fortunately, a heuristic based on the ‘quantized ordering’ approach of Zheng and Chen provides solutions that are near optimal over a broad range of parameter values.

Keywords: Inventory; Production; Stochastic; Periodic review; Continuous review; Backordering

Article Outline

1. Introduction
2. Analysis
3. An approximate approach
4. Discussion and conclusions
Appendix A. Appendix
References






 
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