Modeling Uncertainty in Military Supply Chain Management Decisions

Abstract

This report 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, closedform approximation to the LTD distribution from its components by using mixtures of truncated exponential (MTE) 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 cases where a buyer makes its decisions alone, and later in a situation where members of a two-level supply chain coordinate their actions. Next, a mixture of polynomials (MOP) approach is introduced and utilized to model the LTD distribution for the case of discrete lead time and a daily demand distribution that assumes a standard form. Finally, the MOP model is extended to model an LTD distribution from empirical lead time and daily demand data.