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IMA Journal of Management Mathematics Advance Access originally published online on September 4, 2008
IMA Journal of Management Mathematics 2009 20(3):251-261; doi:10.1093/imaman/dpn023
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An efficient method for calculating the minimum distance from an operating point to a specific (hyperbolic) efficient frontier

Edward A. Silver{dagger}, Diane P. Bischak and Giovani J. C. Da Silveira

Operations Management, Haskayne School of Business, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada

{dagger} Email: edward.silver{at}haskayne.ucalgary.ca

Received on 27 February 2007. Accepted on 30 July 2008.

This paper is concerned with movement from a current operating point so as to reach a 2D efficient frontier. After a discussion of different criteria for deciding on which point on the frontier to target, we focus, as an illustration, on a particular inventory management context and the use of the criterion of minimum distance from the current point to the frontier. Specifically, the efficient frontier turns out to be a hyperbola in a 2D representation of total (across a population of items) average stock (in monetary units) versus total fixed costs of replenishments per year. Any current (or proposed) operating strategy, differing from the class along the frontier, is located above the frontier. Finding the minimum distance from the current point to the frontier requires determining the smallest root of a quartic equation within a restricted range.

Keywords: efficient frontiers; exchange curves; economic order quantity; minimum distance; hyperbola


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