A Min-Max Inventory Model

An inventory model is considered where every N periods an order is placed for an amount which brings the sum of stock-on-hand plus on-order up to some level S. The model treats a single item for which there is random demand. Demands that arrive when there is no positive inventory on hand are back-ordered. Leadtime is treated as random and the receipts of orders are allowed to cross in time.

Values N* and S* which minimize steady state expected costs per unit time cannot be found. In this paper approximations, N₀ and S₀ are found. These are determined by minimizing an expected cost per unit time which has been maximized over all distributions of stock deficit with a given mean and variance. The method is applicable even when the functional form of the distribution of demand is not known. Computer simulations are used to indicate the values of the input parameters for which the expected costs per unit time associated with N₀ and S₀ are close to the similar quantities for N* and S*.