Mixture Distributions for Modeling Lead Time Demand in Coordinated Supply Chains

Abstract

This paper introduces a mixture distribution approach to modeling the probability density function for lead time demand (LTD) in problems where a continuous review inventory system is implemented. The method differs from the typical moment-matching approach by focusing on building up an accurate, closed-form approximation to the LTD distribution from its components by using mixtures of polynomial functions. First, construction of the lead time distribution is illustrated and the approach is compared to two other possible lead time distributions. This distribution is then utilized to determine optimal order policies in a situation where members of a two-level supply chain coordinate their actions.