Title: EOQ extensions exploiting the Lambert W function

Authors: Roger D.H. Warburton

Addresses: Department of Administrative Sciences, Metropolitan College, Boston University, 808 Commonwealth Avenue, Boston, MA, 02215, USA

Abstract: We analyse several extensions to the Economic Order Quantity (EOQ) model: when the inventory deteriorates over time; when the demand contains a stock dependent term; and when the present value, or discounted cost, is included. We derive exact analytical expressions for the order that minimises the total cost, and in each case the Lambert W function arises, adding to the growing list of useful applications for this recently rediscovered function. The analytical solutions have immediate practical and pedagogic applications. [Received 06 September 2007; Revised 13 January 2008; Accepted 01 April 2008]

Keywords: economic order quantity; EOQ model; inventory deterioration; present value; Lambert W function; discounted cost; stock dependent terms.

DOI: 10.1504/EJIE.2009.021584

European Journal of Industrial Engineering, 2009 Vol.3 No.1, pp.45 - 69

Published online: 30 Nov 2008 *

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