Accurate lead time demand modeling and optimal inventory policies in continuous review systems

To construct an accurate probability density function for lead time demand in inventory management models, a mixture of polynomials (MOPs) distributions is estimated using B-spline functions from empirical data on demand per unit time. This is accomplished by summarizing the empirical observations into separate datasets for each lead time value. A mixture distribution approach is then applied to model lead time demand in a continuous review inventory system. Inventory policies can be determined without knowledge of the underlying demand and/or lead time distributions. An improvement to a mixture distribution approach that models the lead time demand distribution with a mixture of truncated exponentials (MTEs) distribution is also presented, and the MOP and MTE techniques are compared. Both methods provide reasonable accuracy, but the MOP approach requires lower computational time to determine optimal inventory policies. The mixture distribution approach is also compared with solutions calculated using optimization through simulation and by compiling a discrete, empirical lead time demand distribution.