Optimization of a Model for an Inventory with Poisson Restocking - Optimization of an Inventory Model -

An inventory supplies stock continuously at a constant rate. A deliveryman arrives according to a Poisson process. If the level of the inventory, when he arrives, exceeds a threshold, no action is taken, otherwise a delivery is made by a random amount. Costs are assigned to each visit of the deliveryman, to each delivery, to the inventory being empty and to the stock being kept. It is shown that there exists a unique arrival rate of the deliveryman which minimizes the average cost per unit time over an infinite horizon.