LIFO Inventory Systems

In many perishable product inventory systems where the issuing of stock to meet demand is controlled by the consumer, the movement of units through the system obeys a LIFO discipline.

In this paper the evolution over time of the LIFO inventory stock age distribution in an environment of stochastic demand is analyzed. The inventory related processes are shown to be completely specified by the random walk ladder height process. This characterization of the LIFO system is then utilized to derive limiting distributions for the stock age distribution when a constant amount is ordered each period. The distribution is found from a Wiener-Hopf integral equation for the ladder height random variable. Transient results for the case of a fixed critical number order policy are also presented. Explicit closed form results are derived for an example in which demand is exponentially distributed. The paper concludes by demonstrating how the results on the steady-state age distribution can be used for devising upper and lower bounds on expected shortages and outdates.