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Net present value analysis of the economic production quantity

Disney, Stephen Michael, Warburton, R. D. H. and Zhong, Q. C. 2013. Net present value analysis of the economic production quantity. IMA Journal of Management Mathematics 24 (4) , pp. 423-435. 10.1093/imaman/dpt002

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Using Laplace transforms we extend the economic production quantity (EPQ) model by analysing cash flows from a net present value (NPV) viewpoint. We obtain an exact expression for the present value of the cash flows in the EPQ problem. From this, we are able to derive the optimal batch size. We obtain insights into the monotonicity and convexity of the present value of each of the cash flows, and show that there is a unique minimum in the present value of the sum of the cash flows in the extended EPQ model. We also obtain exact point solutions at several values in the parameter space. We compare the exact solution to a Maclaurin series expansion and show that serious errors exist with the first-order approximation when the production rate is close to the demand rate. Finally, we consider an alternative formulation of the EPQ model when the opportunity cost of the inventory investment is made explicit.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Centre for Advanced Manufacturing Systems At Cardiff (CAMSAC)
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
H Social Sciences > HF Commerce
Uncontrolled Keywords: economic production quantity; net present value; Lambert W function; Maclaurin series expansion
Additional Information: This article appears in: Special Issue: OR53 Pdf uploaded in accordance with the publisher’s policy at (accessed 05/01/2015)
Publisher: Oxford University Press
ISSN: 1471-678X
Date of First Compliant Deposit: 30 March 2016
Last Modified: 10 Mar 2020 17:20

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