The paper deals with one of the fundamental tasks of logistics, which is finding the answer to the question: “in what quantity it is optimal to resupply the stock” and “when to resupply the stocks” so that the company minimizes its total annual costs resulting from storage. The answer to the first question gives a fairly accurate response both in terms of certainty and in terms of uncertainty. In the case of the search for the answer to the second question the applied method is based on the marginal analysis and leans on the probability distribution of the demand during the delivery time. The theoretical derivation of the correct answers to the above given problems is demonstrated on a simple logistic case study often occurring in practice.