This article illustrates the general problem known as `simulation optimization¿ through an (s, S) inventory management system. In this system, the goal function to be minimized is the expected value of specific inventory costs. Moreover, specific constraints must be satisfied for some random simulation responses, namely the service or fill rate, and for some deterministic simulation inputs, namely the constraint s <S. Results are reported for three optimization methods, including the popular OptQuest method. The optimality of the resulting solutions is tested through the so-called Karush¿Kuhn¿Tucker (KKT) conditions.