In this thesis, we study three periodic-review, finite-horizon inventory systems in the presence of supply and demand uncertainties. In the first part of the thesis, we study a multi-period single-station problem in which supply uncertainty is modeled by partial supply. Formulating the problem under a robust optimization (RO) framework, we show that solving the robust counterpart is equivalent to solving a nominal problem with a modified deterministic demand sequence. In particular, in the stationary case the optimal robust policy follows the quasi-(s, S) form and the corresponding s and S levels are theoretically computable. In the second part of the thesis, we extend the RO framework to a multi-period multi-echelon problem. We show that for a tree structure network, decomposition applies so that the optimal single-station robust policy remains valid for each echelon in the tree. Furthermore, if there are no setup costs in the network, then the problem can be decomposed into several uncapacitated single-station problems with new cost parameters subject to the deterministic demands. In the last part of the thesis, we consider a periodic-review Assemble-To-Order (ATO) system with multiple components and multiple products, where the inventory replenishment for each component follows an independent base-stock policy and product demands are satisfied according to a First-Come-First-Served (FCFS) rule. We jointly consider the inventory replenishment and component allocation problems in the ATO system under stochastic component replenishment lead times and stochastic product demands. The problems are formulated under the stochastic programming (SP) framework, which are difficult to solve exactly due to a large number of scenarios. We use the sample average approximation (SAA) algorithms to find near-optimal solutions, which accuracy is verified by the numerical experiment results. / Thesis / Doctor of Philosophy (PhD)