Inventory Models with Forecasting and Dependent Demand

In general, the single-product inventory model in which demands in successive periods are not independent is difficult to treat. This paper defines a large class of such problems, when there is a positive lead time for delivery, which can be treated by the classical formulation with a single state variable. All results which hold for inventory models with a constant delivery lag can be shown to hold also for this model. An application is made to a system in which demands are generated by part failure and in which a portion of these failures are repaired after a given (constant or probabilistic) time.