In the paper we look into the inventory stock optimization problem within which we focus on conditions of uncertainty. We compare two approaches: 1. we concentrate on the exact approach of a mathematician, who derives his conclusions from a minimum of factual findings and who mostly leans on the formal side of his model; 2. we deal with the same thing applying the "case-based reasoning" approach, which is based on the detailed knowledge and which is understandable to a manager. This comparison enables us to reveal a number of interesting relations and differences. The cooperation of the two approaches enables a deeper insight into the principle of the optimization algorithm. This algorithm is then applied to the practical case study solved under conditions of uncertainty.