An efficient method for calculating the minimum distance from an operating point to a specific (hyberbolic) efficient frontier
Othereconomic order quantity
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AbstractThis paper is concerned with movement from a current operating point so as to reach a two-dimensional, 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 use of the criterion of minimum distance from the current point to the frontier. Specifically, the efficient frontier turns out to be an hyperbola in a two-dimensional 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.
The is a pre-copy-editing, author-produced pdf of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The definitive publisher-authenticated version: E.A. Silver, D.P. Bischak, and G.J.C. da Silveira, “An efficient method for calculating the minimum distance from an operating point to a specific (hyberbolic) efficient frontier,” IMA Journal of Management Mathematics 20:3 (2009), 251–261 is available online at doi:10.1093/imaman/dpn023. Deposited according to policy found on Sherpa/Romeo July 12, 2012.