Letter to the Editor—An Inventory Model for Repair Parts—Approximations in the Case of Variable Delivery Time

The following continuous inventory problem arises in connection with the storage of repair parts. Let demand be for one unit at a time and Poisson, and let delivery time be either fixed or a random variable of known distribution. The size of an order need not be specified until the time of actual production or delivery. The following costs are assumed to be given. A storage cost proportional to quantity of stock and time, a fixed cost of ordering, and a penalty for shortage proportional to the amount of the shortage and its duration. No orders are lost. Alternatively the probability of a loss may be incorporated in the shortage penalty.