EOQ extensions exploiting the Lambert W function

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]