Inventory Model with Fractional Brownian Motion Demand

摘要

This paper studies the inventory model where the demand satisfies fractional Brownian motion. It is an extension of the Master thesis of Buffy Yang of the Department of Industrial Management in the National Taiwan University of Science and Technology in 2009. The purpose of this paper is threefold. First, we point out why the standard derivation of the total demand during the lead time is proportional to the lead time with Hurst exponent. Second, we analytically prove that our proposed inventory model has a unique minimum solution. Third, we demonstrate by simulation for the comparison between our proposed models with the traditional models to indicate that our average saving is about 6%. Our model will provide a better managerial policy for the demand that meets the behavior of fractional Brownian motion.