In most of the early literature dealing with the inventory problems, the research conceptions are mostly concentrated on the continuous review ordering policy. However, viewing the domain of the periodic review inventory policies, it is found that existing literature discussing the problem is not substantial. In order to provide the decision-maker with some perfect managerial strategies of inventory systems, in this thesis, we attempt to investigate the periodic review inventory systems so as to look for their corresponding optimal ordering strategies. In the inventory systems with controllable lead time, when unsatisfied demands occur, in order to reduce lost sales, we consider the supplier could offer a backorder price discount, so that more customers may prefer their demands to be backorders. Or the supplier may invest more capital to reduce lost sales rate through efforts such as staff training, procedural changes, or specialized equipment acquisition. This thesis mainly focuses on the ordering strategies of periodic review inventory models. Under the policies, we propose the inventory models with stochastic demands during the protection interval. In Chapter 2, when unsatisfied demand occurs, we formulate the stockout quantity including backorder price discounts models with controllable lead time. And then, in Chapter 3, we discuss the stockout quantity including backorder price discounts, when the reduction of lead time may accompany the reduction of ordering cost. In Chapters 4 and 5, we consider investing more capital to reduce lost sales rate. In Chapter 4, we formulate the models, including decision variables of periodic review, lost sales rate, and lead time. And in Chapter 5, we formulate the models including decision variables of periodic review, lost sales rate, and target level. For each chapter, we discuss two cases in our formulate inventory models. The first is the case where the demand during protection interval follows a normal distribution. In the second case, where the distributional form of protection interval demand is unknown but merely the mean and standard deviation are known, we apply the minimax distribution free approach to solve the optimal solution. Finally, concluding remarks are made in Chapter 6, and future research directions are proposed.