A Class of One-Period Inventory Models

In most inventory models one of the costs considered is shortage cost. However, this cost is often very hard to measure. For the models considered in this paper, instead of introducing a shortage cost, we define a stock-out penalty function and impose a constraint on it. For example, a constraint on the probability of stock-out can be viewed this way. We exhibit the general, randomized, optimal policy and give graphical and numerical methods of calculating it. We also discuss how our stock-out penalty function is related to shortage cost.