Publisher Summary Inventory theory deals with the management of stock levels of goods, with the intent of effectively meeting demands for those goods. The demands for goods are made by buyers and are met by sellers, regardless of whether monetary exchange is involved. This chapter discusses the stochastic inventory theory. The chapter introduces deterministic economic order quantity (EOQ) model and focuses on the single period newsvendor model. The critical difference in the analyses of these models is the mathematical form of the ordering/production cost function. Many properties of the solution to the newsvendor problem generalize to the case of the proportional ordering/production cost function. When that function is convex, but nonlinear, various reasonable properties of the optimal solution are preserved, but the possibility of using a trivial computation to find the optimal solution tends to fail. The problems are exacerbated when the ordering/production cost function is concave (and nonlinear).