This paper is concerned with two topics: (1) the development of mathematical models for several simple inventory situations, and (2) an industrial application of a mathematical model of inventory. Because T. M. Whitin has described in detail in this journal the present state of research in inventory control (Whitin, T. M. 1954. Inventory control research. Management Sci. I (November).), no attempt will be made to provide a review here. This paper is not an attempt to solve the "general inventory problem." On the contrary, the object is to deal with specific situations, and with an illustrative industrial application. The emphasis is on methodology of approach rather than on a general solution.