An Inventory Model for Arbitrary Interval and Quantity Distributions of Demand

The inventory problem for continuous time is studied under the following assumptions about the demand process (1) an arbitrary distribution of the length of intervals between successive demands; (2) a distribution of the quantity demanded which is independent of the last quantity demanded and any previous events but may depend on the time elapsed since the last demand; (3) unfilled orders are backlogged. The delivery time is fixed. Costs considered are fixed ordering costs and proportional costs of purchase, storage and shortage. The loss function and the equations for reordering point and minimal ordering quantity are derived. Formulae are calculated for the Poisson, stuttering Poisson, geometric, negative binomial, Gamma and compounded distributions.