Double precision rational approximation algorithm for the inverse standard normal first order loss function

Abstract

We present a double precision algorithm based upon rational approximations for the inverse standard normal first order loss function. This function is used frequently in inventory management. No direct approximation or closed formulation exists for the inverse standard normal first order loss function. Calculations are currently based on root-finding methods and intermediate computations of the cumulative normal distribution or tabulations. Results then depend on the accuracy and valid range of that underlying function. We deal with these issues and present a direct, double precision accurate algorithm valid in the full range of double precision floating point numbers.