Mixture distributions for modelling demand during lead time

A mixture distribution approach to modelling demand during lead time in a continuous-review inventory model is described. Using this approach, both lead time and demand per unit time can follow state-dependent distributions. By using mixtures of truncated exponentials functions to approximate these distributions, mixture distributions that can be easily manipulated in closed form can be constructed as the marginal distributions for lead time and demand per unit time. These are then used to approximate the mixture of compound distributions for demand during lead time. The technique is illustrated by first applying it to a ‘normal-gamma’ inventory problem, then by modelling a problem with empirical distributions for lead time and demand per unit time.